CRC Press eBooks

One-Dimensional Motion

Ahmad Amer

Published Nov 5, 2025• 0 citations

Abstract

This chapter explores several cases of one-dimensional quantum motion, emphasizing the physical insights and analytical results. The particle in a rectangular potential well is examined, including the derivation of its quantized energy spectrum and normalization constant, particularly for the case of an infinitely deep well. Comparisons are drawn between the quantum and classical descriptions of motion. The analysis extends to a rectangular potential barrier, where reflection and transmission coefficients are calculated, and the phenomenon of quantum tunneling is explored. The tunnel effect paradox is addressed, along with its applications to α-decay and the cold emission of electrons from metals. Finally, the linear harmonic oscillator is treated in detail, including its energy eigenvalues, eigenstates, parity properties, and zero-point energy — the latter discussed as a consequence of the uncertainty principle and the wave-like behavior of microscopic particles. Metadata/Keywords: one-dimensional motion, rectangular potential well, α-decay, cold emission, quantum tunneling, linear harmonic oscillator, zero-point energy, parity, uncertainty principle, energy eigenstates

DOI: 10.1201/9781003677109-4

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