The transformation rules between a harmonic single‐particle basis and the self‐consistent harmonic approximation in quantum crystal theory are deduced. In the process, the thermal renormalization of the phonon spectrum is calculated to all orders in the phonon‐phonon interaction. The generalization of the transformation technique to a Hartree single‐particle basis is speculated upon.
REFERENCES
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See any text dealing with the quantization of the harmonic oscillator, the lattice vibrations or the electromagnetic field. For instance, L. I. Schiff, Quantum Mechanics (McGraw‐Hill, New York, 1955), 2nd ed., Sec. 46.
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Phonons and Phonon Interactions, edited by T. A. Bak (Benjamin, New York, 1964).
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A. A. Abrikosov, L. O. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Prentice‐Hall, Englewood Cliffs, N.J., 1963).
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© 1973 The American Institute of Physics.
1973
The American Institute of Physics
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