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Community Bot
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@Nick's answer is correct, but redundant.

A state needs not be normalized to begin with, nor be represented by the eigenstates in order to conserve its norm.

Time evolution is a unitary transformation (indeed, because the Hamiltonian is Hermitian). Therefore the norm of a state, any state, is conserved with time. This is explained in detail herehere.

@Nick's answer is correct, but redundant.

A state needs not be normalized to begin with, nor be represented by the eigenstates in order to conserve its norm.

Time evolution is a unitary transformation (indeed, because the Hamiltonian is Hermitian). Therefore the norm of a state, any state, is conserved with time. This is explained in detail here.

@Nick's answer is correct, but redundant.

A state needs not be normalized to begin with, nor be represented by the eigenstates in order to conserve its norm.

Time evolution is a unitary transformation (indeed, because the Hamiltonian is Hermitian). Therefore the norm of a state, any state, is conserved with time. This is explained in detail here.

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yohBS
yohBS
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@Nick's answer is correct, but redundant.

A state needs not be normalized to begin with, nor be represented by the eigenstates in order to conserve its norm.

Time evolution is a unitary transformation (indeed, because the Hamiltonian is Hermitian). Therefore the norm of a state, any state, is conserved with time. This is explained in detail here.