2
votes
1answer
62 views

Eigenenergies and eigenkets given the Hamiltonian

For a two level system the Hamiltonian is: $$ H=a(|1\rangle \langle1|-|2\rangle\langle2|+|1\rangle\langle2|+|2\rangle\langle1|) $$ where $a$ is a number with the dimension of an energy. I need to ...
0
votes
1answer
170 views

Proof of the time-independent Schrödinger equation

I have a question regarding the proof of the time-independent Schrödinger equation. So if we have a time-Independent Hamiltonian, we can solve the Schrödinger equation by adopting separation of ...
2
votes
0answers
139 views

Adiabatic quantum evolution of single photon or biphoton system

The prerequisite for adiabatic quantum evolution of single photon or biphoton system is as follows. We have to prepare a single photon or biphoton quantum system which has a ground and a higher level ...
2
votes
2answers
305 views

How do we know that $\psi$ is the eigenfunction of an operator $\hat{H}$ with eigenvalue $W$?

I am kind of new to this eigenvalue, eigenfunction and operator things, but I have come across this quote many times: $\psi$ is the eigenfunction of an operator $\hat{H}$ with eigenvalue $W$. ...
3
votes
1answer
293 views

How does a state in quantum mechanics evolve?

I have a question about the time evolution of a state in quantum mechanics. The time-dependent Schrodinger equation is given as $$ i\hbar\frac{d}{dt}|\psi(t)\rangle = H|\psi(t)\rangle $$ I am ...
2
votes
1answer
175 views

Perturbation method & eigenvalues

I have a problem but I don't understand the question. It says: "Show that, to first order in energy, the eigenvalues ​​are unchanged." What does it mean? It means that if the Hamiltonian has the ...