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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 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