0
votes
1answer
67 views

Time-dependent perturbation - details in derivation

I get confused about two things when deriving the time-dependent perturbative approach. We have the Hamiltonian $$H = H_0 + \lambda H^{(1)}$$ and we have solved (from Schroedinger) $$\dot{C_f(t)} ...
2
votes
2answers
103 views

Schroedinger equation. Why Potential energy instead of Force?

What is the reason Schroedinger equation is quoted in terms of potential energy instead of force?
0
votes
1answer
176 views

Find the possible energies and corresponding wavefunctions of the Hamiltonian [closed]

The Hamiltonian of an electron stuck within a tunnel in a dialectic cube is found to be $$H=\frac{p^2}{2m}+\frac{1}{2}Kx^2-\frac{e\Phi_0}{a}x$$ Find the possible energies and ...
2
votes
2answers
442 views

Correct application of Laplacian Operator

Not a physicist, and I'm having trouble understanding how to apply the Laplacian-like operator described in this paper and the original. We let: $$ \hat{f}(x) = f(x) + \frac{\int H(x,y)\psi(y) ...
2
votes
1answer
188 views

Degeneracy and the Hamiltonian

How many linearly independent eigenfunctions can be associated with one degenerate eigenvalue of the Hamiltonian operator? (Is there a limit since it contains a 2nd order differential operator?) ...