Questions tagged [superposition]
A basic principle of solutions of *linear* differential (often wave) equations, ensuring that the sum ("superposition") of two solutions is automatically a solution as well. Conversely, solutions (amounting to quantum states in quantum mechanics, since the Schrödinger equation is linear) can be represented as a sum of two or more other distinct solutions, and so can be Fourier/eigenstate resolved to enhance mathematical tractability.
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Vibrating string at many frequencies at once [closed]
I understand standing waves . When it vibrates faster it pushes air faster higher frequency . What about a plucked string? Does different segments have their own standing wave as the string as a whole ...
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Superposition of light beams by $\pi$ phase differences [closed]
What happens if we prepare superposition of two monochrome sinusoidal beams of light which are exactly the same but have $\pi$ differences in their phases? getting nothing?!
$$E_1+E_2 = A\cos(kx-\...
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Interference pattern when particles don't go through either of the two slits, but hit only the mid-portion between the slits and ricochet off! [closed]
'Is it possible to conduct a double-slit experiment in such a way that a series of single electrons/photons) hit only the mid-portion of the two-slits and ricochet off (without entering either slit)? ...
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When does a transition collapse to the final state?
I did my PhD research on device physics of optoelectronic devices. We take the square of
$\langle f| H_{int} |i\rangle $ as the photon absorption probability or the theoretical efficiency of a ...
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Why do Linear Combinations of Atomic Orbitals form *sufficient* approximations of molecular orbitals?
(Assuming no relativistic effects or electron-electron interactions for this question)
First: Am I correct in thinking that Linear Combinations of Atomic Orbitals (LCAOs) are generally good ...
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I don't understand Schrödinger’s Cat [closed]
The main issue I have with the whole "Schrödinger's cat" thing is that the cat has to be either dead or alive. Just because you don't know whether or not it's dead or alive doesn't mean it’s ...
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The relation between Maxwell's equations and the Superposition Principle
My lecturer told us that the statement of superposition has two parts to it:
The Principal of Superposition states that if a charge is placed in the vicinity of many charges, the resultant ...
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Mechanism of Energy Conservation if Two Phase-Offset Photons Sum to Zero-Amplitude [closed]
EDIT: I somehow didn’t notice a cross product sign error, that’s the actual answer to my question. If the two wavefronts have opposing propagation direction and electric field vectors at the time of “...
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Physical terminology for multiplying a wave by a negative number
In physics, given a function $f: \mathbb{R} \to \mathbb{R}$ representing some wave, if we multiply $f$ by a large positive number this might be called amplifying the wave, and if we multiply $f$ by a ...
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How do you find the envelope function for a superposition of two waves or more?
I am trying to determine the envelope function of a superposition of two waves. I will give a concrete example:
Let
$$ f(x, t_1) = \cos(2x + t_1) + \cos(2x + 2t_1) $$
Using a trigonometric identity, ...
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Reasoning for this equality in the Schrödinger equation [closed]
I was doing a question from a quantum mechanics exam from my university for the previous year when I got the following question:
Consider an electron in a one-dimensional square well potential:
$$V(x)...
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Regarding Obtaining Equivalent Resistance using superposition principle
I was working through the electric circuits handouts by Jhan Kalda and encountered the following problem
Now, I do know the standard way to solve such problems, i have seen that method in Wand and ...
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How many layers of superposition can exist?
I was studying quantum mechanics through MIT OpenCourseWare, and the professor explained that any wavefunction can be expressed as a linear combination of different eigenstates, also known as ...
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Stern-Gerlach Experiment with Initial Position Space Measurement
Suppose at time $t = t_0$ I have a spin-1/2 particle in the superposition state
$$
\chi(r,t_0) \otimes (\alpha|\uparrow\rangle + \beta|\downarrow\rangle),
$$
where $\chi$ is the position wavefunction ...
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Can someone help me figure out these superposition equations?
(Please note : while the reply below addresses some of my questions, not all of them have been answered yet. Further contributions are welcome...)
So, in the paper "Bright and dark states of ...
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Fermionic Coherent Superpositions and Parity SSR
According to existing knowledge:
Fermionic coherent superpositions are forbidden due to parity superselection rules (SSR), meaning that a state cannot be physical if it involves a mixture of even and ...
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What is the formula of phase and group velocity for superposition of more than two waves?
I have tried to find formulae for phase and group velocity where more than two waves are superimposed, But could not find anything. Everyone proves the two formulae
$$v_p = \frac{\omega}{k}$$
$$v_g = \...
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To what degree should macroscopic objects be in superposition of position states according to standard quantum theory?
In this review article on objective collapse theories, which is also linked from this Phys.SE post, at least in the part I've read so far, a deal of fuss seems to be made about the fact that we don't ...
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Difference between the superposition of classical complex variable and that of a quantum variable
I was wondering what is the key difference between the superposition of classical complex variables (say for ex. Electric fields) and quantum variables (say for ex. a wavefunction).
Take for example ...
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How to understand correctly the general solution of the Schrodinger equation?
I'm reading Griffiths' Introduction to QM 3rd Edition.
In chapter 2, he mentioned that any linear combination $\psi(x)$ of the solution $\psi_n(x)$ is also a solution to the equation. Then in example ...
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Two Questions on the Double Slit Experiment
Does the distance between the double slit wall, and the detector wall impact the interference pattern on the detector wall?
Intuitively, I think the answer has to be yes, since in the extreme case, ...
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Can a superposition of wave packets describe a single particle?
I have formed a momentum probability density distribution as shown below, and have realised that all the momentum components are positive. It then got me thinking to whether this is allowed.
My ...
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Validity of linear superposition in solving Maxwell's equations
I'm currently reading the book "Electromagnetic Waves and Antennas" by S. J. Orfanidis (publicly available at his own website) and a doubt came to me.
I'm referring in particular to the ...
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What exactly is decoherence?
In quantum mechanics particles that undergo decoherence (breaking of superposition to a definite state) is caused by its interaction with surrounding environment.
In quantum mechanics Superposition is ...
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Confusion in difference between superposition and standing waves
My textbook says for superposition the two waves must be travelling in opposite directions, same is written for standing waves but for interference the waves are shown going in the same direction.
I ...
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Is something wrong with my thinking on why does a wave invert after reflection from a clamped point on a string? [closed]
I have a proof that the reflected wave on a string from a clamped point is inverted of the original wave but I am not sure if it is correct or not. Kindly double check it, I will be thankful.
Consider ...
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Bounds for superposition of mass density?
We start in the Heisenberg picture and take the double time derivative of the position operator (in the $x$ direction) to get an acceleration operator.
$$ \hat a_x= \frac{d^2\hat x(t)}{dt^2} = - \frac{...
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Why is the amplitude of the back wave in Huygens' principle zero?
According to Wikipedia, the Huygens' principle states that:
Every point on a wavefront is itself the source of spherical wavelets, and the secondary wavelets emanating from different points mutually ...
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Confusions about Group Velocity
Recently I'm reading about the difference between phase velocity and group velocity. I straggle to find an understandable derivation of the formula of group velocity (i.e. $v_{g}=\frac{\text{d} \omega}...
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Where is an electron "physically" in superposition? [duplicate]
According to simple Google search:
When an electron is in superposition, its different states can be
thought of as separate outcomes, each with a particular probability of
being observed. An electron ...
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Am I right or wrong about Wheeler's mental retrocausality problem involving one remote star and gravitational lensing?
Tell me where I am wrong.
One of Wheeler’s supposed examples of retrocausality speaks of a remote star, a black hole or other gravitation lens in between it and earth, and astronomers on earth who can ...
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Double slit experiment, interference and definite momentum
I have some troubles in understanding one particular detail concerning double slit experiment: if there is no detector in any slits then after shooting sufficiently many photons (or electrons) on a ...
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How to experimentally measure superposition of a quantum system?
If we have a state in a superposition, e.g. $\lvert \psi\rangle = (1/\sqrt{2})(\lvert\phi_1\rangle + \lvert \phi_2 \rangle)$, how to experimentally measure this superposition? I know that the ...
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What is the shortest path for destructive interference?
Text from a book:
By carefully cutting a single large crystal of silicon (atomic spacing $a = 5.4 \mathring{A} = 5.4*10^{-8} cm$), it is possible to create a series of atomic-scale diffraction ...
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How is the superposition of a photon conserved after passing through a beam splitter?
When a photon hits a beamsplitter, it enters a superposition of either being passed through the beam splitter or reflected off of it. However, it is also my understanding that reflected light imparts ...
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Charge distribution on a conducting sphere
Consider a conducting sphere of radius $a$, with a total charge $Q$ given to it. Obviously, the charge will be uniformly distributed on the surface, resulting in a surface charge density $\sigma_Q = \...
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Superposition of 2 sound wave of same frequency and amplitude, but different waveform
If two waves of same frequency and amplitude but different wave forms(say, a sine wave and a triangular wave) with no phase difference superpose, will it be a resonance? How?
If yes, won't it be a ...
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Relationship between measurement problem and superposition in QM [closed]
Let a quantum system be subjected to a Hamiltonian with a discrete spectrum, such that the system's state vector can be written as a superposition of two of the Hamiltonian's eigenvectors:
$$|\Psi\...
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Schrödinger’s cat theory question [closed]
So, if a CCTV camera is used in the experiment and doesn’t require any contact from outside the box to have access to the film- say it’s files/the video are on an external computer - and the box is ...
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Does wave superposition implies energy conservation? [duplicate]
Imagine a scenario in which two exactly identical but opposite sine wave (basically shifted by a phase of Pi) are superimposing. My question is why isn't the energy conserved here. I mean both the ...
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What does the superposition in the delayed choice quantum eraser experiment look like?
Suppose that we have a double slit experiment, and we fire particles through the double slit and a detector records their position. For simplicity, let's say the screen is partitioned into two areas $...
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How do the entangled photons from an SPDC source behave?
As I understand SPDC sources emit entangled photons, but always in the same polarisation. If this source always outputs this certain polarisation are the photons then still in superposition of each ...
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What state is a particle in before it passes through any Stern-Gerlach devices?
Say we fire some large number N of silver atoms out of a furnace and through a Stern-Gerlach device, which is oriented at some arbitrary angle x. If I understand correctly, then regardless of what x ...
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Phase cancellation in beams of light- edited
I am reading Anil Ananthaswamy's book on double-slit interference and I realized that there's something which I thought I understood about this, but actually do not- as follows:
Photons propagate ...
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How to understand whether an electron in an atom is in superposition, ground or excited state?
As I understand it, defining the orbital of an electron implies that it can be detected with a certain probability in a certain place. But if we take an atom and it is in a superposition state, then ...
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Are some superpositions caused by measurement?
From the Heisenberg uncertainty principle, we know that we can't know both the position and momentum of a particle, does this mean that measuring the position puts the momentum in a superposition? Or ...
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Why do people say the dynamics of quantum mechanics is always linear?
This statement seems false. An example of a non-linear equation governing the dynamics of a quantum system is the Gross-Pitaevskii equation.
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How do gravitational fields combine together in GR?
When we have 2 massive bodies coming close together say 2 black holes or 2 massive stars, how do their respective metrics/spacetime curvature combine in the space in between them?
Do we write
$$G_{\mu\...
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If macroscopic objects weren't in superposition wouldn't they be static?
When we solve the Schrödinger equation we find static solutions for definite energies, and we use those static solutions as a basis for dynamic solutions with uncertain energies.
From this I ...
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How does anti-reflective coating increase light passing through the glass?
How anti-reflective coating works is that it makes the light reflected from the air-coating interface and light reflected from the coating-glass interface cancel each other (destructive interference ...
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