Are degenerate states stationary in quantum mechanics? I know that stationary state means single wavefunction corresponding to single energy. But, what will be in the case of several wavefunctions corresponds to single energy (e.g. degenerate states). are All of them stationary in that case? Can you pls give me explicit difference of stationary state and non stationary?
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The state is called stationary if it is an eigenstate of the Hamiltonian.
Degeneracy is a property of the spectrum of an operator. An eigenvalue is called degenerate if there are at least two linearly independent eigenstates with the same eigenvalue.
Also, when you hear the term degenerate without specifying which operator it applies to, usually it is assumed that this operator is the Hamiltonian.
So yes, degenerate states of the Hamiltonian are by definition stationary, and they have the same energy.
answered Jul 26, 2020 at 6:05
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$\begingroup$ what if hamiltonian contains time dependent potential? $\endgroup$ Commented Jul 26, 2020 at 6:16
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$\begingroup$ @AltuhaAbdu: Just think of the Stern-Gerlach experiment: What we found there is that by changing the Hamiltonian "quickly" the systems wave function can not adapt. Therefore, it is projected/decomposed onto the new eigenbasis. $\endgroup$– NotMeCommented Jul 26, 2020 at 6:43
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$\begingroup$ @AltuhaAbdu if the Hamiltonian changes with time, the eigenstate of $H(t_1)$ are not eigenstates of $H(t_2)$. Also, the eigenvalues change, too. There is no energy conservation. $\endgroup$ Commented Jul 26, 2020 at 10:31