CH110 Study Guide - Final Guide: Matter Wave
In this connection it is instructive to revert to the example
of the harmonic oscillator
considered in Sec. 2. The minimal value of the difference
En − Em for the oscillator is hωc with reference to (2.7).
Placing this value in (4.3) we see that the resonance
occurs when ω =
ωc, which is completely analogous with the classical case.
Here, however, the analogy ends up. If there is no
dissipation of energy, the amplitude of a classical
oscillator tends to infinity
15 when ω → ωc, whereas in the quantum case the
resonant oscillator passes periodically from the mth
eigenstate into the nth eigenstate and vice versa in view of
(4.2). It should be added
that in the general case the quantum resonance occurs if ω
= kωc with k = 1, 2, 3,... .
Having considered the periodic perturbation we now turn
to the case in which the quantum system interacts with an
impacting particle. The above results can be applied
directly to this case too if account is taken of the
undulatory properties of the particle. Let the particle be
described by a plane de Broglie wave, in which case the
frequency ω and the energy of the
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Document Summary
In this connection it is instructive to revert to the example of the harmonic oscillator considered in sec. Placing this value in (4. 3) we see that the resonance. If there is no dissipation of energy, the amplitude of a classical oscillator tends to infinity. En em for the oscillator is h c with reference to (2. 7). occurs when = C, which is completely analogous with the classical case. 15 when c, whereas in the quantum case the that in the general case the quantum resonance occurs if . = k c with k = 1, 2, 3, . frequency and the energy of the. Having considered the periodic perturbation we now turn to the case in which the quantum system interacts with an impacting particle. The above results can be applied directly to this case too if account is taken of the undulatory properties of the particle.
