TransitionProbabilitiesin a Single - Microsystem Consider tMrobability P,-, af transition from an initial time-dependent eigenstate Y,Oaf an unperturbed Hamiltonian H0for a single microsystem (atom or molecule) to a final eigenstate 'Pm0of different energy, under the influence of oerturbation V switched on a t time zero. The conventional derivation riven bv first-order. time-denendent oerturbation theory assumes that the nonstationary state 'P induced by V remains dominated by the initial state n.for any relevant time t after V is switched on, so that the admixture of states m ( f n) into 'P remains small. The authors of a recent paper ( I ) say that at time t, "when the transition from state n to m happens," the state of the microsystem must be dominated by 'Pmocontrary to the above assumption. To avoid this seeming contradiction, they propose that the transition probability .-, is the fraction of such should always be understwd as referring to a macroscopic assembly of microsystems. Then P microsystems in state m, while most remain in the initial state. In fact, the eontradication arises from the phrase quoted above. As explained by various authors (24),experiments usine coberentlv oreoared assemblies show that rnicrosvstems do not suddenlv make a transition from state n to state m. if at time t one makes a measurement with thL~amiltonianto deterrhine the energy of the microsystem, the very process of measurement forces the microsystem to occupy one of the eigenstates of Ho.For an initial state n, thequantity Pa-, gives the probability that the measurement forces the microsystem into state rn. It does not give the probability that the mixed state 'P has evolved into the pure st* 'Pmoimmediately before the measurement. Thus it is not necessary far the textbooks to refer to an assembly in d~seussmgtransition probabilities. I a m grateful t o J. Lee for drawing my attention t o reference ( I ) .
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Literature Cited (11 Cash&,F. L6n. L..Sanchea Ravo, M. N..and Tom,A,, J. CHEM.EDuc.,60,377 (1983) (21 Henderson. 0.. J. C m M . EDUC..56.631 (19791. (3) Macomber. J. D., "The Dynamics of SpectroeeopieTransitions,"Wiley-Interscience, New York,197e Am JPhys, 45,522 (19771. (1) Ailsn, L..and Eberly, J. H. "Optical W n a n c e and Two-kvel A h , ' . Wiley-loteraeienee, New York. 197L
R. W. Munn UMlST
Manchester M6O IQD, UK
644
Journal
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