Relativity and quantization

A. Hr. Anastassov

Yasushi Takahashi, C. L. Hammer

An Introduction to Field Quantization is an introductory discussion of field quantization and problems closely related to it. Field quantization establishes a commutation relation of the field and finds an operator in such a manner that the Heisenberg equation of motion is satisfied. This book contains eight chapters and begins with a review of the quantization of the Schroedinger field and the close relation between quantized field theory and the many-body theory in quantum mechanics. These topics are followed by discussions of the quantization of the radiation field and the field of lattice

V. Aldaya, Manuel Calixto Molina, Julio Guerrero García

Xiaowei Han

From the angle of uncertainty relation,the difficulties in quantization of angular variation in quantum mechanics are analyzed.Hence,the contradiction between quantization of angular momentum and current theory of uncertainty relation is found.

Gustavo V. López, Omar J. P. Bravo

The quantization of the forced harmonic oscillator is studied with the quantum variable (x, v∧), with the commutation relation , and using a Schrödinger’s like equation on these variable, and associating a linear operator to a constant of motion K (x, v, t) of the classical system, The comparison with the quantization in the space (x, p) is done with the usual Schrödinger’s equation for the Hamiltonian H(x, p, t), and with the commutation relation . It is found that for the non-resonant case, both forms of quantization bring about the same result. However, for the resonant case, both forms of quantization are different, and the probability for the system to be in the exited state for the (x, v∧) quantization has fewer oscillations than the (x, p∧) quantization, the average energy of the system is higher in (x, p∧) quantization than on the (x, v∧) quantization, and the Boltzmann-Shannon entropy on the (x, p∧) quantization is higher than on the (x, v∧) quantization.

H. Dieter Zeh