# Questions tagged [wavefunction]

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. DO NOT USE THIS TAG for classical waves.

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### How to calculate the inner product $\langle T|x \rangle = \langle\frac{p^2}{2\mu} |x\rangle$? [closed]

If I have a wave function $\psi (x) = \langle x|\psi \rangle$, now I want to use kinetic energy representation $$T = \frac{p^2}{2\mu} ,$$ where $\mu$ is the mass of particle. I try to \begin{align*...
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### Regarding to the asymptotic solution of quantum harmonic oscillator

In quantum mechanics, the radial equation of the SHO takes the form \begin{align} \frac{d^2 u}{dx^2}+\left(\epsilon-x^2-\frac{l(l+1)}{x^2}\right)u=0, \end{align} where $x=\sqrt{\frac{m\omega}{\hbar}}r$...
1 vote
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### Is the spherical outgoing wave solution to the Schrodinger equation is not a member of $L^2$?

I was reading a discussion about the Mott problem, where the authors discuss the outgoing spherical wave solutions to the Helmholtz equations $\nabla^2 f = - k^2 f$. This equation can also be ...
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### Wavefunction with determinate momentum

In page 100 Griffiths' Introduction to Quantum Mechanics, Griffiths states that the eigenvector of $\hat{p}$ in the position basis is $\frac{1}{\sqrt {2\pi\hbar}}e^{\frac{ipx}{\hbar}}$ and states that ...
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1 vote
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### Why is the time derivative of the wavefunction proportional to a linear operator on it? [closed]

I am currently trying to self-study quantum mechanics. From what I have read, it is said that knowing the wave function at some instant determines its behavior at all feature instants, I came across ...
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### Proof that separation of variables leads to a complete basis of wave function in spherical coordinates [duplicate]

In griffith's introduction to quantum mechanics (chapter 4), there is an analysis of the stationary states of a particle given a potential function $V(r)$ that only depends on the radial distance $r$, ...
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### When solving a paraxial Helmholtz equation ... ? Amplitude vs Wave function

Given the paraxial Helmholtz-equation (PHHE). Why are the solutions formed by the amplitude function of a wave function, but not the wave function itself? Example, a form of a wave function is defined ...
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### Schroedinger equation with value of wave function in polar coordinates?

I'm trying to get a better sense of what causes an increase in the magnitude and phase of the wave function at a given point. Is there a way to rewrite the schroedinger equation such that it ...
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### Is the overall (distinguishble-particle) ground state for a many-body identical particle Hamiltonian also immediately the bosonic ground state?

Consider the following many-body Hamiltonian of $N$ particles in an external trapping potential with inter-particle interactions: \begin{align} \hat{H}= \sum_{i=1}^{N} \left[-\frac{\hbar^2}{2m} \...
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1 vote
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### Self-interference of nuclear decay

Consider a stationary atom undergoing radioactive decay. The probability density function for decaying at time $t$ is given by an exponential distribution: $$p(t)=\lambda e^{-\lambda x}$$ When ...
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### Does QM recognise empty waves?

If a particle (photon) goes through a Mach-Zehnder interferometer it is accepted in quantum mechanics texts that in passes in both channels after first beam splitter BS1 and propagates there until BS2....
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### Homogeneity of Schroedinger equation implies norm conservation

I am trying to understand how homogeneity of Schroedinger equation implies norm conservation. I know that we are considering the non-relativistic case, where particle number is conserved, so we do not ...
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### Group velocity, phase velocity and signal velocity for axion like particles

In dark matter models of axion-like particles (ALPs), sometimes we get the field $$\phi=2\phi_0\sin(m_\phi c^2 t/\hbar)\cos(k_\phi x)$$ This is like an stationary field with amplitude $\phi_0$ (in m/s ...
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### Scattering Matrix and the Lippmann-Schwinger equation in QM

I am currently studying scattering theory from the Sakurai's quantum mechanics. I have previously studied this subject from Griffith's quantum mechanics. In the latter textbook, scattering matrices ...
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