Tagged Questions

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Calculating the expectation value of a Hamiltonian

I want to calculate the expectation value of a Hamiltonian. I have a wave function that is $$\psi = \frac{1}{\sqrt{5}}(1\phi_1 + 2\phi_2).$$ I want to know if I set this up properly. The ...
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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 ...
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Change of operator in the Hamiltonian [closed]

We are told that the particle has mass m and charge e and is moving in 2 dimensions. The position operator $\mathbf{X}=(X_{1},X_{2})$ and momentum operator $\mathbf{P}=(P_{1},P_{2})$ We are given ...
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Energy Spectrum of pair of spin-1/2 particles with general Hamiltonian

I found this problem, and so far I am stumped. I was wondering if anyone wanted to solve it with me, or help me calculate eigenvectors, or just give insight on my questions. Consider a system of ...