Eigenvalues and eigenkets of a two level system

1. The problem statement, all variables and given/known data

The Hamiltonian for a two level system is given:

H=a(|1><1|-|2><2|+|1><2|+|2><1|)

where ‘a’ is a number with the dimentions of energy.

Find the energy eigenvalues and the corresponding eigenkets (as a combination of |1> and |2>).

2. Relevant equations

H|ψ>=E|ψ>

3. The attempt at a solution

Using |a>=∑ci |a’>

I wrote |ψ> as a combunation of the two system kets |ψ>=c1|1>+c2|2> (c1,c2 are complex numbers).

so H|ψ>= a(|1><1|-|2><2|+|1><2|+|2><1|)*(c1|1>+c2|2>)= a(c1|1>-c2|2>+c2|1>c1|2>)=a ((c1+c2)|1>+(c1-c2)|2>)=E|ψ>.

How do I continue?

Thank you 🙂
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

http://ift.tt/1cLLWS2

Leave a comment

Your email address will not be published.


*


Show Buttons
Hide Buttons