On the Adiabatic Theorem in Quantum Theory Part I

Cover On the Adiabatic Theorem in Quantum Theory Part I
On the Adiabatic Theorem in Quantum Theory Part I
Kurt Otto Friedrichs
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9) holds. Then we introduce an operator J^ ' (8. 10) (n>Uf *^Mn-)= [h3(n')-h3(n")] "^n' 1 i n734^')- K34"Mn" ) for n' 4 n", eliJ -37- (8. 11) (nlj^^^-'^Mn) = Note that h (n' ) 4 h (n") for n' 4 n'*, as assumed in Section 2 .
It is then clear that the operator J^ ^^, in place of J^ ', s ' -^ s satisfies equation (8, 8) .
The diagonal terms of J^ ' are evidently not deter- mined by condition (8. 8). In fact, J^ ' is uniquely determined by equation (8, 8) only except for the addition of an arbitra
...ry operator which commutes with h (N ), and hence is a function of N .
so o Thus we may write (8. 12) jf *1) = J«*li . A

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