# 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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158 views

### Superposition of Magnetic fields in a Transformer

Lets say we have a transformer with two primary coils. The coils are positioned end to end such that unlike poles are adjacent (NS or SN). The current in one of the coils has a phase shift of 90 ...
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### Sound beats mathematical expression

I am reading about sound beats. According to the superposition principle, if at a certain position the two waves are given by, let say, $$\ y_a(t)=Asin(2\pi f_at)$$ $$\ y_b(t)=-Asin(2\pi f_bt)$$ ...
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### How to best describe wave behavior on even dimensions?

Main source: http://www.mathpages.com/home/kmath242/kmath242.htm On this article, as far as I understand, the author claims that wave behavior on even dimensions would give rise to many waves with ...
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### Mach-Zehnder interferometer reaction to input light with polarization state ±45˚?

We have a Mach-Zehnder interferometer with two non-polarizing beam splitters. The polarisation state of the input beam is a superposition of +45˚ and -45˚ polarizations. In the upper arm of the ...
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### Can any type of wave produce an interference pattern from two sources?

Can any type of wave produce an interference pattern similar to the one in a double slit experiment? So for example, could a radio wave create an interference pattern through the airwaves?
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### Full solution of the wavefunction for the particle in a box problem

The particle in a box problem is a common question that people are taught in order to get some practice using Schrödinger’s equation. For this kind of problem one usually solves the equation for ...
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### Quantum Computing, and if a Q-bit can be entangled and in superposition at the same time

I was wondering if a Q-bits can be in both entangled and in superposition at the same time?
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### Assumption in the derivation of Schrödinger's equation

I read on the "derivation" (with some assumptions) of the Schrödinger equation. The idea is to start from $$T + U = E$$ wher $T$ is kinetic energy, $U$ is potential energy, and $E$ is total energy. ...
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### How to conduct the electron double slit experiment

I am planning to conduct the electron double slit experiment for a project in my school. Even after researching quite a bit online, I wasn't able to find a proper guide that explains the materials and ...
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### Can a superposition of a travelling wave and a standing wave give a standing wave?

I have two similar questions: 1) I have heard, that a travelling wave can be understood as a superposition of standing waves. Can you exaplain this (some images would be wonderful)? 2) Can a ...
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### Never ending quantum superposition? [closed]

So I am wondering over the Copenhagen Interpretation how can a decoherence or measurement ever happen. If in the beginning of the universe everything was in a state of coherence being in ...
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### Supposing that a quantum system is in a degenerate ground-state, is it valid to call this a “superposition” of the possible groundstates?

According to the adiabatic theorem, a quantum system can be prepared in the ground-state of some Hamiltonian $H_f$ if it starts in the ground state of some Hamiltonian $H_I$ and is varied "slowly" ...
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### Direction of wave propagation unchanged after superposition?

It's quite confusing.Principle of superposition states that the amplitude of two superposing wave eqauls their indivisual amplitude vector sum.But what about direction.Souldnt't wave direction of ...
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### Why is electrostatic force a function of the product of charges, not the sum?

When you have two forces , you ADD them to get the total. If both of us push on a car, the total force on the car is the sum of our forces. But, If we have an electron approaching another electron, ...
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### Linear and non-linear systems

When I read about the superposition principle, it says that it works only on linear systems, my problem is that I cannot really understand the difference between a linear and a non-linear system. I ...
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### Rules of addition of electric field

According to the principle of superposition of Electric Fields , we know that Electric fields add using laws of vectors. However while adding the electric fields , if for example one field is ...
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### Is this assertion by Landau and Lifshitz's QM equivalent to the axiom that state spaces are vector spaces?

Many expositions of Quantum Mechanics begin by stating axioms of the following type: "The state of a quantum mechanical system is given by a nonzero vector in a complex vector (or Hilbert space) ...
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### Double-Slit experiment and the role of observation in the distribution

so I am still having difficulty understanding the role of measuring/observing the wave function. Many of the videos I have watched says that when we are not looking at the wave function it makes an ...
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### Quantum theories related to superposition of entire events

If science, by accident or design, was to discover that the superposition of particles we already know of scales up to entire events (so different events are in superposition in the future, with some ...
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### Can only one particle exist at a defined point in spacetime?

And for the contrasting question, may two or more particles be superimposed at the same point in spacetime?
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### What do Quantum Physicists mean by this? [closed]

When it comes to the mystical field of quantum physics, I am often told that a particle system, such as an electron, can exist in many states at once and is thus able to occupy many different volumes ...
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### Why are wave packets constructed so that the maximum probability occurs at K0 (the average wave number)?

The definition of a wave packet I have been given is that it is "a superposition of many plane waves, with wave numbers grouped around an average value $k_0$". I was told that, for a particle we want,...
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### Why we take the term with cosine of $(α-β)/2$ in amplitude modulation term rather than $(α+β)/2$? [closed]

In case of beats Why do we take cos$\frac{α-β}{2}$ component in modulation of amplitude and not the cos$\frac{α+β}{2}$ term?
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### Does “natural” superposition of particles exist?

While studying the basics of quantum computers, I came across Hadamard gates and learned, that these gates are used to put qubits into superposition meaning that these qubits are both, 0 and 1 at the ...
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### Superposition of polarized photon

I understand that a $+45^\circ$ polarized photon is a superposition of $0^\circ$ (vertical) and $90^\circ$ (horizontal): $|\!+\!45\rangle = 0.707 (|H\rangle + |V\rangle)$. So measuring the ...
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### Electric potentials and superposition

I had a question regarding the addition of electric potentials. Consider two positively charged particles $q_1$ and $q_2$ at distance $R$ apart. Let the charges have magnitudes $q_1$ and $q_2$. For a ...
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### It's a wave packet a superposition of standing waves? How is the wave packet in 3d (real world)?

The wave function who is non zero in a finite space, who represent the free particle, Is it formed by the interaction of standing waves or travelling waves? And a second question: everybody describes ...
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### Does the total sound intensity increase when reflected?

In a closed pipe and sound it produced at one end of the tube and the other reflected the sound. If you measure the intensity within the pipe would it be greater than if there would be no reflection ...
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### Meaning of phase relationship for a superposition of states

I have studied an introductory course in quantum mechanics, and yet I still do not understand the significance of a phase difference between quantum states that a system is in a superposition of. In ...
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### Beat frequency of superimposition of three sine waves

Basically we have the function $$f(t)=\sin(2π\nu_1 t)+\sin(2π\nu_2 t)+\sin(2π\nu_3 t)$$ Let $T$ be the fundamental period of $f(t)$. Beat frequency is defined as the number of peaks in intensity ...
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### Superposition of waves whose wavelengths are continuous

I know how to find the resultant waves when finitely or countably many waves are superimposed but how do I find the wave equation when there are infinitely many waves whose wavelength is continuous? ...
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### Is Light intangible to other Light? And how does all the intersecting light exist in space?

I was thinking of how light actually gets into my eyes, and thought about my light bulb shining rays to every part of my bedroom wall, and reflecting them towards me. but then i realized, i could be ...
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### Do we hear anything special when the beat frequency is in audible range, but the sounds producing the beats are not? [duplicate]

When the beat frequency is very low, we hear periodic maxima and minima. Our ear cannot perceive a on-off like sound when its frequency is more than 10 Hz. So, beat frequency in audible range will not ...
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### Superposition of position eigenstates after measurement of position?

In a discussion with someone recently, the person made the following statement: Even when we observe a particle, it is still in superposition of position states within the resolution of the ...
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### Would we observe beats if the ratio of the frequencies of two waves is irrational?

For Example, Would we observe beats for a 540 Hz sound wave and a 545.879614.....(irrational) wave? Though they lie within 10Hz of each other, their sum would not produce a periodic function so I don'...
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### Calculating the possible values of momentum (and their associated probabilities) if the wavefuntion is not an eigenstate of the momentum operator?

I am working through some problems to practice for an upcoming quantum mechanics exam. I do not understand how, in general, one splits the resulting wavefunction of an operator which is not an ...
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### Why do i always get resultant electric field by differential form of Gauss law?

The electric field in differential form of gauss law is the resultant electric field due to a continuous charge distribution. and the law states that the divergence of electric field at any point is ...
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### Superposition of waves and energy transferred

A wave transfers energy. I was reading about the superposition of two waves, where the amplitudes of the two waves added up to produce a resultant wave. So I began wondering about the energy that is ...
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### How to derive the time frequency and the spatial frequency when two waves undergo the beat phenomenon? [closed]

What approach would give the time frequency and spatial frequency of the beat?
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### Do all waves superpose on each other?

What would happen if two waves with different frequency were to pass through 1 point in space at the same time? Would they interfere at that point in space? Are superposition and interference the same ...
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### Can all waves interfere with each other? What conditions must two waves have such that they interfere?

Do they need to have the same frequency or amplitude? Should they pass through a given space at the same time? Should they have the same sources?
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### Why doesn't superselection forbid almost every superposition?

A superselection rule is a rule that forbids superposition of quantum states. As stated by Lubos here, one cannot superpose states with different charges because of the conservation of charge: An ...
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### Quantum Tunneling, Superposition, and The Uncertainty Principle

After looking through various papers and articles on explanations of quantum tunneling I've been left wondering about one thing. I've read explanations of tunneling as an affect of a particles wave ...
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### Quantum superposition follows from energy conservation? (possibly not a crackpot question. It's just an area of research in the fundamentals)

This question is inspired by research in resource theories of coherence, research in quantum thermodynamics and its connection to coherence, and section 10.1 (The Adiabatic Theorem) in Griffiths. The ...
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### Can we see “imaginary” light beams?

When a reference beam, R, interferes with an object beam, O, the interference pattern is captured by a holographic plate. When reconstructing the image, the reference beam is incident on the ...
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### When plane waves interfere, is the resulting wave also a type of plane wave? [closed]

An object reflects light from a beam, U_1 (a plane wave). I would like to, as simply as possible, describe the light reflected by the object. Can I describe the reflected light, U_2, as a plane wave? ...
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### Coherent superposition of mass eigenstates of neutrinos in neutrino oscillations

What is the physical meaning of coherent superposition of mass eigenstates of neutrinos? And why it is necessary for the oscillation of neutrinos? Why can't an incoherent superposition of mass ...