What is the theoretical proof of the quantization of the energy of electromagnetic field?
- From: "Tareq" <ask.about.islam@xxxxxxxxx>
- Date: 16 Mar 2007 11:42:11 -0700
The energy of the quantum mechanical harmonic oscillator is proved to
be quantized after solving the Hermite equation and discovering that
normalizable solutions of the wavefunction exist only for a discrete
spectrum of energy. When the electromagnetic field is quantized in the
beginning of any textbook on Quantum Optics, (see for example Zubairy
and Scully), the field is supposed to be inside a bounded cavity and
is decomposed into the normal modes of this cavity. The conjugate
coordinates and momentum that comprise the field Lagrangian are
converted into operators and the commutation relations between qi and
pi, namely: [qi,pj]=ih.delta ij are imposed on generalized coordinate
and momentum. The operators a, a+ are directly produced from these
generalized coordinates and momenta and by writing the Hamiltonian of
the field we discover that it's of the same form of the hamiltonian of
the mechanical quantum harmonic oscillator and then jump to the
conclusion that the energy of the EM field is also quantized and the
operators a, a+ are creation and annihilation operators!
Is this a sound proof for the quantization of the energy of
electromagnetic field? I don't think so...
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