# Homework Help: Energy Spectrum for Hamiltonian

1. Dec 11, 2008

### degerativpart

1. The problem statement, all variables and given/known data
Find the energy spectrum of a system whose Hamiltonian is
H=Ho+H'=[-(planks const)^2/2m][d^2/dx^2]+.5m(omega)^2x^2+ax^3+bx^4

I gues my big question to begin is what exactly makes up the energy spectrum. I know the equation to the first and second order perturbations but Im not sure exactly what the energy spectrum entails. Please help.

2. Relevant equations

3. The attempt at a solution
ive figured out that H'=ax^3+bx^4

and Ho==[-(planks const)^2/2m][d^2/dx^2]+.5m(omega)^2x^2
and lambda=1 which mean ita a full perturbation

2. Dec 11, 2008

### turin

In QM, "energy spectrum" is just a stupid word that they use to mean the set of possible energy eigenvalues. I personally hate that terminology; it's so misleading.

I don't know what this means.

3. Dec 11, 2008

### degerativpart

haha obviously I agree with you and I read that the lambda in the equation for H=Ho+(lambda)H' when equals to zero means its an unperturbed equation and when it is equal to 1 then its fully perturbed. I dont know I read it.
But I guess my next question how many energy eigenvalues are there? Does that mean I should probably only go to the second oreder corrections?

4. Dec 12, 2008

### turin

How many eigenvalues are there for H0? Can the perturbation remove or add any, or does it just shift them?

5. Nov 13, 2010

### softnix

Sorry, I could say that book is the question?. thank you.