All Questions
3
questions
1
vote
0
answers
43
views
Quantum Mechanical PDE Question
I'm studying quantum mechanics and I'm considering the usual time-independent Schrödinger equation
\begin{equation*}
-\left(\frac{\hbar^{2}}{2m}\right)\left(\nabla'\right)^{2}u_{E}(\mathbf{x}') + V(\...
- 11
2
votes
0
answers
108
views
Spectrum of $H = - \Delta + y^2 + a e^{b(x+y)}$.
Define the Hamiltonian
$$
H = - \Delta + y^2 + a e^{b(x+y)}\,,
$$
where $- \Delta = - \partial_x^2 - \partial_y^2$ and $a,b > 0$. I'm trying to determine the spectrum and/or generalized ...
- 2,949
3
votes
2
answers
274
views
Book on periodic Schrödinger operators
I am looking for good books about the spectral theory of periodic (1-dimensional) Schrödinger operators on a compact interval.
A good reference I found was Reed/Simon Analysis of Operators (and a ...
user66906