1
vote
1answer
99 views

Quick question on perturbation theory

Suppose we have a particle in an infinite potential well, with $V(x) = 0,\space 0< x < a $ and infinity everywhere else. Now suppose we have a perturbation on the LHS of the well: $V_1(x) = v, ...
0
votes
1answer
66 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
1answer
75 views

The expansion of a function in powers of a parameter

In the perturbation theory for non-degenerate levels, the energy $E_n(\lambda)$ of an eigenstate $|\psi_n(\lambda)\rangle$ of the hamiltonian $\mathcal{H}=\mathcal{H}_0+\lambda \mathcal{H}_1$ (where ...
5
votes
3answers
230 views

Time Varying Potential, series solution

Suppose we have a time varying potential $$\left( -\frac{1}{2m}\nabla^2+ V(\vec{r},t)\right)\psi = i\partial_t \psi$$ then I want to know why is the general solution written as $\psi = ...
3
votes
1answer
665 views

Time-Dependent Potentials in Quantum Mechanics

A potential that depends on time is usually solved using the time dependent perturbation theory in standard undergraduate textbooks in quantum mechanics. The reason usually mentioned is that time ...