|Apr1-03, 02:19 AM||#1|
Ground State Wave function
Why is that, the ground state eigenfunction in ANY quantum mechanical system is symmetric under inversion of co-ordinates?
|Apr1-03, 06:04 PM||#2|
so let s assume that you had asked this question about any quantum system with a symmetric hamiltonian.
when there is a symmetric hamiltonian, all eigenfuctions must be either even or odd. that is, they must be either symmetric or antisymmetric.
an antisymmetric wavefunction necessarily passes through zero. therefore it has a node, therefore it cannot be the ground state.
therefore the ground state must be symmetric.
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