# Tagged Questions

A complex scalar field that describes a quantum mechanical system. The square of the modulus of the wave function gives the probability of the system to be found in a particular state.

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### Rectangular window $\psi$ wave-function and the calculus of $\langle p^2\rangle$ for it

I'm currently considering a rectangular window $\psi$ function: $$\psi(x) = \begin{cases}\left(2a\right)^{-1/2}&\text{for } |x|<a \\ 0&\text{otherwise.} \end{cases}$$ I am interested in ...
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### Wave/particle-duality as result of taking different limits of a QFT

There is an account on dualities in quantum field theories and string theories by Polchinski from last week http://arxiv.org/abs/1412.5704 At the end of page 4, he writes the wave/particle ...
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### The wave function of transverse one is different from longitude one for convenience?

I use the book Fundamental of Physics Hallidays&Resnick 10th Edition Jearl Walker to study in my physics class while I got myself University Physics with Modern Physics Sears, Zemansky 13th ...
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### Are wave functions real physical objects? [duplicate]

Are wave functions (ex. electron waves) real physical objects or just mathematical tools?. Some researchers say that they have proof that they are real objects. Here's [the link] (http://www.nature....
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### Wave function in quantum mechanics

I was wondering about something while studying quantum mechanics. If the wave function collapses when measuring a particle and assumes a single position, how do we know that it was a wave in the first ...
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### Why two-particle wavefunctions are separable and their corresponding particles are indistiguishable at the same time?

If the wavefunction $\psi(r_1,r_2)$ doesn't represents an entangled state, it is separable: $$\psi(r_1,r_2)=\psi_a(r_1)\psi_b(r_2)$$ In this treatment, we ignore the interaction between two particles ...
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### How to minimize the wavepacket dispersion?

This is a final exam problem. Here is what I can remember: We know that if an electron's wavefunction starts out as a narrow wavepacket, and moving in a region of constant potential, then the ...
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### Allowed energies for semi-harmonic oscillator

Question: If a particle is attached to a semi-harmonic oscillator (that is, for example, the spring is stretchable but not compressible) such that the potential $V(x)$ is infinity for $x\leq0$ and ...
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### Is $\phi_n =\left\langle \vec r | n \right\rangle$ the photon wave function?

I am a bit confused about this issue and I am still not clear whether is there is a photon wave function or not. Since we use Fock states $| n \rangle$ to represent the state of a quantized ...
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### Does there exist a hyperbolic relationship between frequency $\omega$ and wavenumber $k$?

As the title states, is it possible to derive a hyperbolic relationship in the form of $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ between frequency $\omega$ and wavenumber $k$ I have tried to start this ...
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### How does a Wavefunction collapse?

I have been wondering and researching... How does a wavefunction collapse into one state?More specifically, what conditions cause a wavefunction for a quantum particle to collapse? Does this have to ...
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### Hilbert space and Hamiltonians

Assume a system described by a Hamiltonian H, and assume that the eigenstates of H, $φ_i$(r) are integrable in absolute square. We say that these states belong to a Hilbert space (they can even form a ...
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### Quantum Wavefunctions Without Space

A handful of physicists have a rather peculiar definition of 'nothing' in terms of cosmology. Their claim is that the Universe, assuming it has 0 total energy, could have arisen from nothing but ...
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### Estimate of the second shallowest bound state?

Suppose we have a 1D potential $V(x)$ of finite range, i.e., $$V(x) ~=~0$$ for $|x| > b$. The potential is assume to support at least two bound states, but might have more, say $n\geq 2$. ...
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### How to know if a wave function is physically acceptable solution of a Schrödinger equation?

How does one decide whether a wave function is a physically acceptable solution of the Schrödinger equation? For example: $\tan x$ , $\sin x$, $1/x$, and so on.
### 1D Finite potential well: solutions with $\sinh$ and $\cosh$?
So I am studying the (one dimensional) quantum mechanical finite potential well defined by: $$V(x) = \cases{0, &|x|>a\cr -V_0, &|x|<a}$$ where $V_0>0$ is a real number. I know ...
How does one derive the fact that $$\psi(t,x) = (\tfrac{2 \pi \hbar t}{m})^{-d/2}\int_{\mathbb{R}^d} e^{im\tfrac{(x-y)^2}{2\hbar t}}\psi_0(y)dy$$ is a solution of the time-dependent free ...