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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.

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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What happens to the energy when waves perfectly cancel each other?

What happens to the energy when waves completely cancel each other out via destructive interference? It seems like the energy just disappears, but that would violate the law of energy conservation. My guess is that the kinetic energy is transformed…
aortizmena
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How is a quantum superposition different from a mixed state?

According to Wikipedia, if a system has $50\%$ chance to be in state $\left|\psi_1\right>$ and $50\%$ to be in state $\left|\psi_2\right>$, then this is a mixed state. Now, consider the state…
Ruslan
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Why do travelling waves continue after amplitude sum = 0?

My professor asked an interesting question at the end of the last class, but I can't figure out the answer. The question is this (recalled from memory): There are two travelling wave pulses moving in opposite directions along a rope with equal and…
Dylan
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Differences between pure/mixed/entangled/separable/superposed states

I am currently trying to establish a clear picture of pure/mixed/entangled/separable/superposed states. In the following I will always assume a basis of $|1\rangle$ and $|0\rangle$ for my quantum systems. This is what I have so far: superposed: A…
ftiaronsem
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Extension of Schrödinger's cat thought experiment

My question is quite simple. In the thought experiment of Schroedinger's cat: When the scientist measures the state of the cat, its wavefunction collapses into either the alive or dead state. But wouldn't then the scientist in turn be in a…
Loreno Heer
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Why is Huygens' principle only valid in an odd number of spatial dimensions?

Apparently Huygens' principle is only valid in an odd number of spatial dimensions: https://mathoverflow.net/a/5396/21349 Huygen's principle in curved spacetimes Why is this? [EDIT] This is somewhat perplexing, since AFAIK it's pretty common to…
user4552
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What is the reason that Quantum Mechanics is random?

We know quantum mechanics gives a random result when we observe a particle that's in a superposition, but why is it random? One of the explanations I've heard is that because light comes with those discrete energy packets called photons, when a…
Andrew.Wolphoe
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If a thousand people whisper inaudibly, will the resulting sound be audible?

If a thousand people whisper inaudibly, will the resulting sound be audible? (...assuming they are whispering together.) I believe the answer is "yes" because the amplitudes would simply add and thus reach an audible threshold. Is this right? if…
SAH
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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 measured some other observable $O$, and found me in…
Juan Perez
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Linearity of quantum mechanics and nonlinearity of macroscopic physics

We live in a world where almost all macroscopic physical phenomena are non-linear, while the description of microscopic phenomena is based on quantum mechanics which is linear by definition. What are the physics points of connection between the two…
Andy Bale
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How can Schrödinger's cat be both dead and alive?

So, this goes to something so fundamental, I can barely express it. The Schrödinger's Cat thought experiment ultimately asserts that, until the box is opened, the cat is both dead AND alive. Now, this is obviously ludicrous. The cat either died or…
White Prime
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Do all waves of any kind satisfy the principle of superposition?

Is it an inherent portion of defining something as a wave? Say if I had something that was modeled as a wave. When this thing encounters something else, will it obey the principle of superposition. Will they pass through each other?
JobHunter69
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Why do electrons in an atom occupy only the stationary states?

When we talk about the elementary problems in quantum mechanics like particle in a box, we first calculate the energy eigen-function. Then we say that the most general state is the linear combination or superposition of these basis eigen-functions.…
Girish Pahwa
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Can particles be in a superposition of times as well as positions?

We often talk about the various possible positions a particle can have upon measurement according to the probability density. But owing to the profound link of space and time in relativity, why do you never hear of possible temporal superpositions?
mebaker
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Energy conservation and interference

I have a problem with energy conservation in case of interfering waves. Imagine two harmonic waves with amplitudes $A$. They both carry energy that is proportional to $A^2$, so the total energy is proportional to $2A^2$. When they interfere, the…
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