How to calculate the transition rate

by Nastenka
Tags: kets, quantum field theory, quantum mechanics
Nastenka is offline
Jul15-12, 09:47 AM
P: 1
1. The problem statement, all variables and given/known data
I have the usual equation for the transition amplitude:
A=< k|exp(-iHt)| j>,

while my Hamiltonian in Dirac notation looks like:

H=\sum E_a|a><a|+\sum_b (E_b|b><b|+V_1|0><b|+ V_2|b><0|)

In order to find the transition rate I should take a derivative as:
dA/dt, so that I will get something like:

A=< k|-iH*exp(-iHt)| j>

2. Relevant questions

Now, my question is:

how to treat it further?

3. The attempt at a solution

I know I should expand it with series for the exponent, but then I obtain in the middle this:
-iH(1+H)=-iH-iH2 that confuses me. I feel I am stucked in such an easy task. But the proble is that I cannot expand it with eigenvalues and eigenvectors which would simplify a lot my task....
Phys.Org News Partner Science news on
Simplicity is key to co-operative robots
Chemical vapor deposition used to grow atomic layer materials on top of each other
Earliest ancestor of land herbivores discovered

Register to reply

Related Discussions
Calculate CO bond length from J=0 to J=1 transition Biology, Chemistry & Other Homework 4
Calculate natural line width of the transition Advanced Physics Homework 4
Optical transition rate for quantum wells Atomic, Solid State, Comp. Physics 0
QM : Transition Prob -> Decay Rate Advanced Physics Homework 0
calculate rate? Introductory Physics Homework 2