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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Basic confusion about evolution of wave function of a free particle
I am going through Griffith's introduction to quantum mechanics. An example for a free particle is given where
$$\Psi(x,0) = \begin {cases}A \quad \text{if } x\in [-a,a]\\ 0\quad \text{otherwise}\end{...
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Are projective representiations of a Lie group a representation of the semi-direct product of the group with $U(1)$ if the norm is preserved?
Let's say we have a function $f(x_{\mu},t)$ that transforms under the action of an $N$-parameter group $G(a_{\nu})$. Then a projective representation of $G(a_\nu)$ in the $f(x_\mu,t)$ basis would ...
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Momentum Eigenvalues for Particle in a Box
A question from my college exams is as follows:
Find out the eigenfunctions and eigenvalues of the momentum of a particle of mass $m$ moving
inside an infinite one-dimensional potential well of width ...
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Is a fermionic boson possible?
We know that bosons need an overall symmetric wavefunction. So is it possible for a boson to have an anti-symmetric spatial wavefunction and an anti-symmetric spin wavefunction? Such that upon ...
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Basic doubt in quantum mechanics
Do entities like electrons, which are considered point particles in Classical Mechanics, actually have a definite position at a particular time (irrespective of it can be measured or not)?
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Functional analysis question about operator on quantum wave functions
If I have two time-independent wave functions $\psi_{t_{1}}$ and $\psi_{t_{2}}$ and define an operator $\hat{U}$ such that $$\psi_{t_{2}} = \hat{U}_{t_{1},t_{2}}(\psi_{t_{1}})$$ and $$\psi_{t_{2}}(x) =...
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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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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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Can any meaning be given to a path integral with no fixed end point?
A path integral has the interpreted as the probability a particle goes from $A$ to $B$ in time $t$. Such a path integral is given by
$$\langle x_B, t|x_A, 0\rangle = \frac{1}{Z} \int_{\textrm{paths } ...
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A simple question in quanum mechanics on position and momenum eigenstates
The eigenfunctions (eigenstates) for the momentum of a particle are given by the plane waves
$$\phi(x,t) = \sin(kx - \omega t)$$
If we sum a large number of these waves in a range from $0$ to $k_m$, ...
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Closed expression of eigenfunctions of a two dimensional isotropic harmonic oscillator
Where can one find the closed expression of the eigenfunctions of the 2d isotropic harmonic oscillator?
I saw something like this:
$$ \psi_{n_r m }(r, \theta) \propto e^{im\theta} r^{|m|} e^{-r^2/2} F(...
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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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