Unformatted text preview: / ( sin( 2 ) 2 / ( ) ( n L x n L L L x n L L x x n n − = − = − = ± Parity Operator: The parity operator is the operator that takes x →-x as follows: ) ( ) ( x x P op − = . In the above problem the wavefunctions ψ ± are eigenfunctions of the parity operator with eigenvalues ±1 as follows: ) ( ) ( x x P n n op ± ± ± = . If the Hamiltonian H is invariant under x →-x then the eigenvalues of the parity operator are constants of the motion. In this case we say that “parity is a good quantum number” ( i.e. it is conserved ) and as a function of time “+” states remain “+” states and “-” states remain “-” states. E 1 = E n + = 1 Energy Levels n-= 1 E 2 = 4E E 3 = 9E n + = 2 + - +...
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- Spring '07
- mechanics, lowest energy state, lowest energy, parity operator