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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Why, in low energy situations like atomic physics, are massive particles found to be in integer number states?

In quantum field theory electrons are conceptualized as quantized excitations of the quantum electron field. Generically the electron field can be in a superposition of number states. This is related ...
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Does a waveform of frequency $f+\Delta f$ beat against a wave of frequency $2f$?

In the elementary treatment of waves, beating occurs between two waves of similar frequencies because $$\cos(2\pi f_1 t)+\cos(2\pi f_2 t) = 2\cos(2\pi \frac{f_1+f_2}{2}t)\cos(2\pi \frac{f_1-f_2}{2}t)$$...
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Path integral and interference pattern

I would like to ask you to shed some light on an aspect of the famous Young's slit experiment. It seems to me that the "feynmanian" quantization method allows to obtain observational ...
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Phase of the standing wave constituents

Do 2 superimposed waves have to be 180/0 degree apart to form a standing wave? It seems to be the necessity for forming nodes of 0 displacement (taken that their amplitudes are the same) but can they ...
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How do different $|\text{Alive}\rangle+|\text{Dead}\rangle$ kind of states behave under decoherence?

I am looking for literature that investigates said behaviour for spins. So far I found many papers on how to measure the macroscopicity of states and therefore a classification of macroscopic states. ...
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What is the effect of changing the volume of a permanent magnet in the vicinity of an electromagnet?

If I have a single Neodimium permanent magnet, held at a fixed distance (gap distance) from the end of an energised coil, what would be the effect of adding a second magnet to the back side of the ...
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How to correlate the frequency of source to The frequency of particle just between the two medium while transmission and reflection of wave?

When a pulse travels through rarer to denser medium,two new waves (reflected and transmitted) are formed from incident wave,While the wavelength of the Transmitted wave differs from wavelength of ...
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Basics | Does the velocity in throwing direction change [closed]

Disregarding air resistance. The mass of the ball is centered, not inequally distributed, it can be seen as one mass point for this question! The ball is thrown on earth, just to be exact. When ...
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How do the entangled photons behave?

If I place a linear polarizer at 45° angled with respect to linear axis in front of a KDP crystal then, will the photon pair that the crystal produce be entangled in superposition of linear and ...
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Which interpretation of quantum physics interprets superpositions in the sense of "an object *really* being in two places at once"? [closed]

In popular scientific literature one often reads of "objects being in two places at once" as a verbal way of explaining superposition of states (in the mathematical view of elements of a ...
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"Different" energy eigenstates - clarification of meaning? (re: 't Hooft sort of)

After reading this paper: https://link.springer.com/article/10.1007/s10701-021-00464-7 "Fast Vacuum Fluctuations and the Emergence of Quantum Mechanics" Gerard ’t Hooft I was struck by a ...
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When an electron is in superposition what happens to its charge?

Hi my question is simple, what happens to the charge of an electron when it is in superposition, I am saying this because when orbitals of electrons are in superposition they still have charge to make ...
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Why does a sound of two sources of same-amplitude come out louder than one-source sound with the same amplitude?

Sorry if the question is stupid. The last time I touched physics was in school and I have never come back to it since. But this question popped up just recently in my life and I realized I don't know ...
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Feynman’s QED explanation of reflection from a small mirror

In the “QED: The strange theory of light and matter” professor Feynman explains at page 45 and following how the simple rule introduced in the first chapter can explain the geometrical law of ...
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What do we mean when we say gravitational waves are non-linear and do not superpose like EM waves?

I have read this question: Now it's not actually true that general relativity obeys a law of superposition, but it is an extremely good approximation for a small-amplitude gravitational wave passing ...
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Superposition of two electromagnetic waves

If an electromagnetic wave in isolation with vector potential $A^1_{\alpha}$ satisfies the wave equation $\Box A^1_{\alpha}=0$, how do we construct the total electromagnetic wave that results from ...
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Are magnetic fields additive?

When considering the field around a permanent magnet or current carrying wire, would it be accurate to say the magnetic field effects of each element add linearly in space, or is the interaction ...
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Combine the completeness and linearity of Schrodinger equation's solution, can we say that any wavefunction can solve any Schrodinger equation?

From quantum mechanics, I learnt: Completeness of energy eigenfunction: The energy eigenfunctions of the Schrodinger equation span the space, i.e. any state can be expanded as linear combination of ...
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If arbitrary wavefunctions can be expanded as energy eigenfunctions of a schodinger equation, is it mean that it can solve schodinger equation anyway? [closed]

We know that the superpostion of solutions also sloves the schodinger eq, and any wavefunction can be expended as superposition of energy eigenstates. Is it means that any wavefunction can solve the ...
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Magnetic superposition in transformer

Magnetic superposition in transformer core if they are saturated But if we have permanent magnet in circuit will it show superposition Will magnetic field add up ?
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If we apply a magnetic field to a core saturated by a permanent magnet, what will happen? [closed]

If we apply a magnetic field to a core saturated by permanent magnet, will the magnetic field of the permanent magnet and electromagnet get combined? I mean to say superposition will be applied?
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Are there any nonlinear Schrödinger equations?

The 1D Schrödinger equation reads: $$\frac{\partial \Psi}{\partial t}=\frac{i\hbar}{2m}\frac{\partial^2 \Psi}{\partial x^2}-\frac{i}{\hbar}V\Psi.$$ Now, generally we have $V=V(x)$ (or it dependending ...
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What determines if something is subject to probabalistic/superimposition behavior?

The position of electrons, or behavior of photons, is probabilistic, allows for superposition of states, and follows Schrödinger's equation for their wave functions. But other particles like protons ...
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Wigner function in relation to real space

The Wigner function is a quasi-probability distribution because it can have values of $x$ from -1,0,+1. As it is orthogonal to the $x,p$ plane can this be represented as a dipole moment along the $z$ ...
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What happens if the eraser polarization filter is moved with randomness generated by observation of particles in superposition in famous experiment?

I was reading the book The outer limits of reason by Nosin S. Yanofsky and I stumbled upon this experiment. There's a wall with two holes (S1 and S2) with a polarization filter on the right of the ...
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How can we superpose waves neglecting spatial parts?

I was reading H. J. Pain's book on the Physics of Vibrations and waves. He introduced the concept of the group velocity by superposing two waves of amplitude a, frequencies $\omega_1$ and $\omega_2$ ...
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Does the "particle in a box" necessarily form a standing wave?

I am reading Randall D. Knight's "Physics for Scientists and Engineers" textbook, and he claims that if matter has wave properties, then a particle in a box will form a standing wave. He ...
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Does destructive interference of photons destroy energy? [duplicate]

I am wondering about if two light beams comes in opposite phases exactly against each other, destructive interference will happen. From what I have found on the internet many say that energy is not ...
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Why do I see $\frac{1}{\sqrt2}$ a lot in QM?

A lot of books and papers in QM use $\frac{1}{\sqrt2}$ in equations. If we want to calculate the intensity of a light or some probability, I see this irrational value every where. why do we use this ...
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Sound waves adding up [duplicate]

If there is a swarm of bees, why is it louder than a single bee? This question may sound stupid but ... if they are all buzzing at the same frequency with the same loudness and the phases of the sound ...
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Superposition principle in classical collision theory

While reviewing my notes for a test, I stumbled upon a statement which I could not justify. In a diagonal two dimensional collision between a particle and a wall (considering the wall's mass as being ...
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In a quantum state with 50-50% probability, can the outcome ever be determined with any law or logic? Or should it always be a random value? [closed]

Please help me here. If the probability is 50-50%, the outcome can only be a random one. And a random outcome can never be determined by any laws or rules of physics. And if I'm not wrong, quantum ...
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Does the Multiverse Theory rely on Superposition?

Note: I'm not asking if the Multiverse Theory and the MWI are the same thing, cf. e.g. this Phys.SE post. If I understand it correctly, the Multiverse Theory doesn't rely on the Many Worlds ...
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According to the MWI, does the universe always split with all possible outcomes or only splits for those particles that were observed?

Sorry in advance if this is a stupid question. The Many World Interpretation (MWI) says that, at every point in time, the universe splits into a multitude of existences in which every possible ...
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Path Integral QM and Destructive Interference

In Shankar's QM book pg. 224, it was said that the contributions $Z=e^{iS[x(t)]/\hbar}$ add constructively near the classical path $x_{cl}(t)$ since the action $S[x_{}(t)]$ is stationary here. As we ...
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What exactly is meant by the quality of a qubit?

When looking at a quantum annealer, we can see that D-Wave solutions have produced an annealer with over 5000 qubits whilst other companies that take a quantum gate approach have only managed 127 (IBM)...
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A contradiction in the Babinet principle, an even more mysterious phase difference

This is a continuation of a previous question I asked.. So, as we know the Babinet principle states that the superposition of the screen and its complement is the same as the unobstructed light. This ...
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Schrodinger equation of linear combination of quantum states

We know that the solution for $i\hbar \frac{\partial}{\partial t}|\psi (t) \rangle = H|\psi (t)\rangle $ where $H$ is time-independent Hamiltonian, is $|\psi(t)\rangle = e^{-iHt/\hbar}|\psi(t=0)\...
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Superposition principle for the electric field

I had read somewhere that superposition principle is valid for linear functions, but the electric field is not a linear function, then why is the superposition principle valid for electric field?
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Does the standing wave equation proof require $\ell=Nλ$? [closed]

Consider two identical sources $S_1$ and $S_2$ of waves, separated by a distance $\ell$ (as shown in the figure). The sources produce waves in opposite directions(and towards each other). Now, ...
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Am I in a superposition?

Someone looks at me. Now, they know my position and my momentum, with some uncertainty. Therefore, they haven't measured either my position nor my momentum, since neither is known perfectly. They ...
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Superposition of momentum plane waves for a WF: discrete of continuous?

On the one hand there is a theorem that states that any reasonable wave function $\Psi$ can be written as a superposition of eigenstates of $\hat Q$ (a hermitian operator). So if $\Psi _i$ are the ...
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Coherence and superposition principle - equivalent properties?

I'd like to revisit a question I posted earlier. While I now know what coherence means (and how it can be defined) I still struggle to give an intuitive explanation that goes along with the word "...
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System in Superposition, Subsystem in Eigenstate: are the variables real/determined or non-real/undeterminate?

As far as I can tell, this is all textbook Quantum Mechanics, no interpretations were assumed. Isolated system $S$ is divided into 2 isolated, separable sub-systems: $Particle$ and $Observer$. $...
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On the superposition of forces [closed]

Isn't force just a vector quantity? Don't vectors of the same kind add according to the superposition principle? So why don't all forces obey the superposition principle?
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Superposition v/s Superimposition

What is the difference between 'superposition of waves' and 'superimposition of waves'?
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From discrete to continuous superposition of waves, what happens to omega?

The Wikipedia page on group velocity uses the superposition of two cosines (of slightly different wavenumbers and angular frequencies) to show that group velocity $v_g = \frac{d\omega}{dk}.$ The sum ...
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Superposition of EM waves and "magic" behind tuned receiver circuit

I'm struggling to understand how the receiver circuit (eg. FM radio) is able to extract a particular frequency out of the sum of all received frequencies by its antenna? I've checked dozen of websites,...
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Superposition Intuition

As I have understood so far, contrary to classical mechanics, quantum mechanics never gives you the exact position of a 'particle' but only a probability that the particle is in a certain area. Thus ...
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Superposition of waves for changing frequency [closed]

Is this physically correct statement that the "superposition of waves increases with increasing frequency". An increase in frequency means smaller wavelength --> smaller path differences ...

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