I have a problem on the basis of quantum mechanics and it's so simple that I'm almost too afraid to ask. Anyway:(adsbygoogle = window.adsbygoogle || []).push({});

1.) Schrödingers differential equation is used for time indepent and time depent problems. The solution is a wave function or the linear combination of the resulting wave functions, but not a vector.

2.) The Eigen Value equation. Here the solution are states which are vectors and the Hamiltonian is a matrix.

My problems are:

1.)When becomes the Hamiltonian a matrix? If the spin is taken into account and the Hamiltonian can be expressed in terms of the Pauli matrices? Are there any other potentials that can be written in matrix form?

2.) The density of states is the sum over all eigen states. If these states are vectors, the density becomes a matrix. Here again: Is the density a matrix if the spin is regarded or are there any other examples, spin states excluded, where the density can written in matrix form?

Thanks for attending to my embarrising problem

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# Schrödinger equation: eigen value or differential equation

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