Tagged Questions
2
votes
2answers
108 views
How do we know that $\psi$ is the eigenfunction of an operator $\hat{H}$ with eigenvalue $W$?
I am kind of new to this eigenvalue, eigenfunction and operator things, but I have come across this quote many times:
$\psi$ is the eigenfunction of an operator $\hat{H}$ with eigenvalue
$W$.
...
1
vote
0answers
26 views
Quantum graph theory: complex spectra
In quantum graph theory, what are the properties of a given graph to own complex conjugated complex eigenvalues, either finite or infinite? Spectral graph theory is as far as I know a not completely ...
1
vote
1answer
84 views
Mysterious spectra?
In my blog post Why riemannium? , I introduced the following idea. The infinite potential well in quantum mechanics, the harmonic oscillator and the Kepler (hygrogen-like) problem have energy spectra, ...
10
votes
3answers
319 views
How to tackle 'dot' product for spin matrices
I read a textbook today on quantum mechanics regarding the Pauli spin matrices for two particles, it gives the Hamiltonian as
$$
H = \alpha[\sigma_z^1 + \sigma_z^2] + ...
3
votes
1answer
129 views
How does a state in quantum mechanics evolve?
I have a question about the time evolution of a state in quantum mechanics. The time-dependent Schrodinger equation is given as
$$
i\hbar\frac{d}{dt}|\psi(t)\rangle = H|\psi(t)\rangle
$$
I am ...
3
votes
5answers
224 views
Math of eigenvalue problem in quantum mechanics
I learned the eigenvalue problem in linear algebra before and I just find that the quantum mechanics happen to associate the Schrodinger equation with the eigenvalue problem. In linear algebra, we ...
1
vote
0answers
73 views
2D quantum well energy spectrum (analytical vs numerical)
I am trying to understand the energy spectrum difference between the analytical and the approximated solution for a quantum well.
The particle is inside a box with domain $\Omega=(0,0)$X$(1,1)$. For ...
3
votes
2answers
214 views
Quantum Mechanics Notation for BRA KET
I've been given this homework problem, but I do not understand its notation.
Please perform the following where the wavefunctions are the normalized eigenfunctions of the harmonic oscillator ...
4
votes
2answers
223 views
Eigenvalues of a quantum field?
Fields in classical mechanics are observables. For example, I can measure the value of the electric field at some (x,t).
In quantum field theory, the classical field is promoted to an operator-valued ...
1
vote
2answers
203 views
Angular Momentum Operators Non-Degenerate
Typically one writes simultaneous eigenstates of the angular momentum operators $J_3$ and $J^2$ as $|j,m\rangle$, where
$$J^2|j,m\rangle = \hbar^2 j(j+1)|j,m\rangle$$
$$J_3 |j,m\rangle = \hbar ...
2
votes
2answers
358 views
Non-Degeneracy of Eigenvalues of Number Operator for Simple Harmonic Oscillator [duplicate]
Possible Duplicate:
Proof that the One-Dimensional Simple Harmonic Oscillator is Non-Degenerate?
I'm trying to convince myself that the eigenvalues $n$ of the number operator ...
2
votes
1answer
103 views
Perturbation method & eigenvalues
I have a problem but I don't understand the question. It says:
"Show that, to first order in energy, the eigenvalues are unchanged."
What does it mean?
It means that if the Hamiltonian has the ...
1
vote
0answers
28 views
Random quantum systems with asymmetric Lifshitz tails?
For a quantum mechanical system with a periodic Hamiltonian (Schrödinger operator) $H$, let $N(E)$ be its integrated density of states, i.e. the fraction of eigenvalues in the spectrum $\sigma(H)$ ...
2
votes
1answer
78 views
When does the “norm of quasi-eigenvectors” matter in calculations? For which physical results are these even used?
Which physical system in nonrelativistic quantum mechanics is actually described by a model, where the norm of the "position eigenstate" (i.e. the delta distribution as limit of vectors in the ...
2
votes
1answer
97 views
Are Quantum Physics and statistical theory always the same as semiclassical approximations?
Quantum Mechanics and Statistical physics is a bit hard , could we then study only the WKB approximation ?
In the form:
replace $ \sum_{n=0}^{\infty}exp(- \beta E_{n})=Z(\beta)\sim\iint ...
1
vote
2answers
109 views
eigenvalue staircase and hamiltonians
Let two Hamiltonians $H_{1}$ and $H_{2}$ be defined in such a manner that their eigenvalue staircases satisfy
$ N_{1} (E) = N_{2} (E)+A +O(E^{-1})$
What can we say about their potentials $ V_{1} ...
20
votes
4answers
756 views
In quantum mechanics, given certain energy spectrum can one generate the corresponding potential?
A typical problem in quantum mechanics is to calculate the spectrum that corresponds to a given potential.
Is there a one to one correspondence between the potential and its spectrum?
If the ...
