Unformatted text preview: “lowering operator” to the lowest energy state gives > − >= − h   ) ( E d E a op . But there is no state with energy lower than E which implies that d = 0 and  ) ( >= − E a op . Now we can solve for E as follows > >= >= + >= − + 2 1 2 1    ) ) ( ) ( (  E E E E a a E H op op op h h h . Hence, h 2 1 = E and we normalize so that 1  >= < E E . Excited States: All the other states are calculated from the ground state using the “raising operator” as follows: > >= +  ) ( ! 1  E a n E n op n and > + >= n n op E n E H  ) (  2 1 h and hf n n E n ) ( ) ( 2 1 2 1 + = + = h Planck’s guess was E n = nhf!...
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 Spring '07
 FIELDS
 mechanics, Energy, op, lowest energy state, op H op

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