Classical regime | Quantum regime | Explanation for quantum effects | |
Black-body radiation | The Rayleigh-Jeans law [Man, p.253, (10.21)]. However, experimental results contradict the Rayleigh-Jeans prediction [Eis, p.13, Fig. 1-8]. | Wien's law [Man, p.254, (10.23)]. | Planck's radiation formula [Man, p.250,
(10.14)].
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The wave-particle duality | The Rayleigh-Jeans law [Wu, p.41, l.2]. | Wien's law [Wu, p.41, l.1]. | Considering the energy fluctuations of Planck's law, Einstein derives [Wu, p.40, (1-13)] which is the sum of two mean-squares of fluctuations: one from the wave property and the other from the particle property. Thus, Planck's law reveals the simultaneous presence of both the wave and particle properties of radiation. Based on [Lan2, p.79, l.10; p.80, (32.15)], Planck proposes [Wu, p.41, (1.14)(ii)]. See [Wu, p.41, l.11-l.15]. [Wu, p.41, (1-14)] directly relates a electromagnetic wave to to its particle properties [Wu, p.41, l.17-l.19]. |
The photoelectric effect | 1. The maximum kinetic energy of
a photoelectron is independent of the intensity of illumination. 2. Existence of a cutoff frequency. 3. The absence of a time lag. |
E=hn [Eis,
p.30, l.- 7-p.31, l.15]. K= hn - w [Eis, p.30, (2-3)]. |
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The Compton effect | l ® ¥ Þ Rayleigh scattering dominates [Eis, p.38, l.-4]. | l ® 0Þ Compton scattering dominates [Eis, p.39, l.3]. | E=hn [Eis, p.34, l.27-p.35, l.6]. |
X-ray production | h® 0 Þ l min® 0 [Eis, p.42, l.-15]. | Existence of a minimum wavelength [Eis, p.41, Fig. 2-10]. | E=hn [Eis, p.41, l.- 3-p.42, l.10]. |
Pair production | hn ³ 2m0c2 [Eis, p.44, l.8-l.11]. | [Eis, p.47, (2-17) & Fig. 2-15]. | |
Simple harmonic oscillators | [Eis, p.138, l.2 & p.165, Fig. 5-19]]. | [Eis, p.137, l.-19]. | The time-independent Schroedinger equation only allows certain energy values [Eis, p.161, Fig. 5-14]. |