Symmetric properties time-dependent Schrodinger equation

If the wave function for the system is initially symmetric (antisymmetric), then it remains symmetric (antisymmetric) as time progresses. This property follows from the time-dependent Schrodinger equation... 

Since the Hamiltonian is symmetric in space coordinates the time-dependent Schrodinger equation prevents a system of identical particles in a symmetric state from passing into an anti-symmetric state. The symmetry character of the eigenfunctions therefore is a property of the particles themselves. Only one eigenfunction corresponds to each eigenfunction and hence there is no exchange degeneracy. 

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