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## Main Question or Discussion Point

Hi,

The energy of the quantum mechanical harmonic oscillator is proved to

be quantized after solving the Schrodingers equation which leads to 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]=i hbar.delta ij are imposed on the 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. We 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 of photons!

Is this a sound proof for the quantization of the energy of

electromagnetic field? I don't think so...

The energy of the quantum mechanical harmonic oscillator is proved to

be quantized after solving the Schrodingers equation which leads to 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]=i hbar.delta ij are imposed on the 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. We 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 of photons!

Is this a sound proof for the quantization of the energy of

electromagnetic field? I don't think so...