# 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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471 views

### What is the wavefunction of the Young Double Slit experiment?

I have never seen the wavefunction for this experiment and would like to know how to derive it using the Schrodinger equation. I specifically want to see how the electron wave function leaves the ...
2answers
686 views

### When can we assume that the wavefunction is separable

While working out the stationary states of a single particle in a 3d infinite potential box ($V=0$ inside a cuboid of known dimensions, $V=\infty$ everywhere else), I realized I had to assume the ...
4answers
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### What does the Schrodinger Equation really mean?

I understand that the Schrodinger equation is actually a principle that cannot be proven. But can someone give a plausible foundation for it and give it some physical meaning/interpretation. I guess I'...
1answer
451 views

### Virial theorem and variational method: a question

I have an hydrogenic atom, knowing that its ground-state wavefunction has the standard form $$\psi = A e^{-\beta r}$$ with $A = \frac{\beta^3}{\pi}$, I have to find the best value for $\beta$ (...
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### Superconducting Wavefunction Phase (Feynman Lectures)

In Volume 3, Section 21-5 of the Feynman lectures (superconductivity), Feynman makes a step that I can't quite follow. To start, he writes the wavefunction of the ground state in the following form (...
5answers
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### Hydrogen radial wave function infinity at $r=0$

When trying to solve the Schrödinger equation for hydrogen, one usually splits up the wave function into two parts: $$\psi(r,\phi,\theta)= R(r)Y_{l,m}(\phi,\theta).$$ I understand that the radial ...
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487 views

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### Ground state of Spherical symmetric potential always have $\ell=0$?

I was given a problem where I have a spherically symmetric potential (the exact form is not relevant to this question, I think - but anyway is it 0 for $r\in[a,b]$ and $\infty$ everywhere else) and I ...
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515 views

### Floquet quasienergy spectrum, continuous or discrete?

I haven't got a feeling about Floquet quasienergy, although it is talked by many people these days. Floquet theorem: Consider a Hamiltonian which is time periodic $H(t)=H(t+\tau)$. The ...
1answer
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### Bohr-Sommerfeld quantization from the WKB approximation

How can one prove the Bohr-Sommerfeld quantization formula $$\oint p~dq ~=~2\pi n \hbar$$ from the WKB ansatz solution $$\Psi(x)~=~e^{iS(x)/ \hbar}$$ for the Schroedinger equation? With $S$ the ...
3answers
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### Does quantum mechanics allow faster than light (FTL) travel?

Let's suppose I initially have a particle with a nice and narrow wave function[1] (I will leave these unnormed): $$e^{-\frac{x^2}{a}}$$ where $a$ is some small number (to make it narrow). Let's also ...
2answers
425 views

### Why must $\Psi (x,t)$ go to zero faster than $\frac{1}{\sqrt{|x|}}$?

Why must $\Psi (x,t)$ go to zero faster than $\frac{1}{\sqrt{|x|}}$ as $|x|$ goes to $\infty$? According to Griffiths' Introduction to Quantum Mechanics, it must. I don't understand why, and this is ...
2answers
580 views

### Non-separable solution for the Schrödinger equation

Schrödinger solutions are usually if not always of the type: $\psi=\operatorname{T}(t)*\operatorname{X}(x)$ (we use the separation of variables method to arrive at the time independent Schroedinger ...
2answers
205 views

### What state the wave function collapses into after an inaccurate measurement?

I'm watching MIT online lectures Quantum Physics I (roughly from one hour mark in the video). The lecturer explains wave functions that describe "Stationary States" that consist of a single energy ...
2answers
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### Physical position eigenfunction normalisation

We know that the Dirac function $$\delta(a)=\lim_{a \rightarrow 0} \delta_{a}(x)$$ can be written as an infinitesimally narrow Gaussian: $$\delta_{a}(x) := \frac{1}{\sqrt{2\pi a^2}}e^{-x^2/2a^2}$$ ...
1answer
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### Mathematical definition of wavefront in case of non harmonic waves

What is the general mathematical definition of wavefront? Wavefront is the surface where, at fixed time, the phase is constant But for non-harmonic waves we cannot talk about phase as the ...
1answer
268 views

### Which position and momentum distributions arise from some wave function?

Consider a particle in one dimension with wave function $\psi(x)$. The probability density function describing how likely it is to find it in a given position is given by $f(x)=\left|\psi(x)\right|^2$....
5answers
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### Is the wave function of a particle re-created after a measurement stops?

Yeah, I haven't quite understood, or been told, what happens to, for example an electron and its wavefunction, when you stop to measure it. I mean, an electron has a wave function describing its ...
2answers
319 views

### Wavefunctions in different Hilbert spaces

The state of a quantum system is represented by a wavefunction usually in some specific Hilbert space, .e.g of position, spin, momentum etc. But before deciding in which of these bases to decompose ...
3answers
601 views

### Confusion about wavefunction separability

A wavefunction is inherently a multi-particle function. If you have a container that is perfectly isolated from the external universe (not possible, but just imagine it) and filled with $n$ particles,...
3answers
3k views

### Momentum of particle in a box

Take a unit box, the energy eigenfunctions are $\sin(n\pi x)$ (ignoring normalization constant) inside the box and 0 outside. I have read that there is no momentum operator for a particle in a box, ...
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### Is it guaranteed that wavefunction is well behaved everywhere?

I don't really know much about Quantum mechanics, but would like to know one simple fact. The state function $\Psi(r, t)$ whose magnitude gives the probability density of the position of the particle ...
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986 views

### How is the Pauli Exclusion Principle a consequence of antisymmetric wavefunction?

How is the Pauli Exclusion Principle a consequence of antisymmetric wavefunction?
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448 views

### Does a wavefunction interact with itself?

Considering the double slit experiment with a charged particle, after the particle passes through the slits, do the two portions of the wavefunctions feel the electromagnetic attraction of the other ...
1answer
303 views

### Can general wavefunctions be expressed as kets?

I am confused on bra-ket notation in quantum mechanics. My professor says that a ket is an eigenfunction of some operator. However, for some time now I thought a ket could represent a general ...
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373 views

### Confusion about 1-forms as introduced in “Gravitation” (Kip S. Thorne,…)

In the book Gravitation in chapter 2, paragraph 5, they introduce the concept of 1-forms by thinking about the momentum 4-vector differently. They first introduce the de Broglie 1-form as follows (I ...
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324 views