By Professor Dr. Walter Greiner (auth.)
Quantum Mechanics - An Introduction lays the principles for the remainder of the direction on complicated quantum mechanics and box concept. ranging from black-body radiation, the photoelectric impression, and wave-particle duality, Greiner is going directly to speak about the uncertainty kinfolk, spin, and many-body structures; he contains functions to the hydrogen atom and the Stern-Gerlach and Einstein-de Haas experiments. the math of illustration thought, S matrices, perturbation idea, eigenvalue difficulties, and hypergeometric differential equations are offered intimately, with eighty four totally and punctiliously labored examples and routines to consolidate the fabric. This fourth version has been revised and makes the ebook up to date again.
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Extra resources for Quantum Mechanics: An Introduction
Transformation of units cal 1. 52 x lOIS (K)4 or T ~ 6000 K . (11) 2. 4 Wien's Displacement Law Problem. e. Amax T = const. from Planck's spectral energy density ~ dE/ dw. Here Amax is that wavelength where ~ dE/ dw achieves its maximum. Interpret the results. Solution. We are looking for the maximum of Planck's spectral distribution: d dw [1V dE] dw 3(exp (nw) )-1] kBT -1 d [ nw dw JT2C3 = = 3nw2 [exp JT 2 C3 (~) _1]-1 kBT n exp(nw/kBT) --=0 JT 2 C 3 kBT [exp(nw/kBT) _1]2 nw 3 ]-1 ::::} 3 - -nw exp ( -nw ) [ exp ( -nw ) - 1 kBT kBT kBT With the shorthand notation x 20 ex (1) = nw/kBT, we get the transcendental equation (2) ' which must be solved graphically or numerically.
23) dk 2 ~ 0 , for a certain time, we can assign a particular fonn to the wave packet. Then we can consider the matter-wave group as moving as a whole with the group velocity vg . Following de Broglie, we assign to each unifonnly moving particle a plane wave with wavelength A. 2). 25) meaning that we must know the rest mass of the particle in motion to determine its wavelength. 122 x 10- 8 cm. 8 later on). The shorter the wavelength, the shorter the distance is between two points that can be seen distinctly through the microscope.
A) The wavelength A = 27rI k of a particle of mass m is related to its momentum p; the latter is determined by the total energy E using p = j(Elc)2 -m5c2 . i[(Elc)2 -m5c2rl/2 . For photons mo = 0 and therefore Aph = 27rncl Eph. In the nomelativistic limit, we get for electrons and neutrons p = J2mOEkin, and thus A = 27rnJ2moEkin . rradiation we have AphOO keY) = 120 pm, AeO keY) = 39 pm, AN(5 eV) = 13 pm . (b) Replacing the X -radiation by neutrons of the same wavelength leaves the scattering angles unaltered at first.
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