What Defines the Energy Spectrum in a Hamiltonian System?

[degerativpart]

Homework Statement

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 I am not sure exactly what the energy spectrum entails. Please help.

Homework Equations

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

 

[turin]

I gues my big question to begin is what exactly makes up the energy spectrum.

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.

and lambda=1 which mean ita a full perturbation

I don't know what this means.

 

[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 don't 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?

 

[turin]

... how many energy eigenvalues are there?

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

 

[softnix]

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