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# Quantum Mechanics (4th Edition)

## Alastair Rae

Language: English

Pages: 309

ISBN: 0750302178

Format: PDF / Kindle (mobi) / ePub

Continuing the exceptional tradition of the previous editions, Quantum Mechanics, Fourth Edition provides essential information about atomic and subatomic systems and covers some modern applications of the field. Supported by a Web page that contains a bibliography, color versions of some of the illustrations, and links to other relevant sites, the book shows how cutting-edge research topics of quantum mechanics have been applied to various disciplines. It first demonstrates how to obtain a wave equation whose solutions determine the energy levels of bound systems. The theory is then made more general and applied to a number of physical examples. Later chapters describe the connection between relativity and quantum mechanics, give some examples of how quantum mechanics has been used in information processing, and, finally, discuss the conceptual and philosophical implications of the subject. New to the Fourth Edition: · A chapter on quantum information processing that includes applications to the encryption and de-encryption of coded messages · A chapter on relativistic quantum mechanics and introductory quantum field theory · Updated material on the conceptual foundations of quantum physics containing discussions of non-locality, hidden variables, and parallel universes · Expanded information on tunneling microscopy and the Bose-Einstein condensate Presenting up-to-date information on the conceptual and philosophical aspects of quantum mechanics, this revised edition is suitable both for undergraduates studying physics, chemistry, or mathematics and for researchers involved in quantum physics.

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Alt. ISBN:9780750308397

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discussion of such predictions and we shall find that the theory is successful in every case; in fact the whole of atomic physics, solid state physics and chemistry obey the principles of quantum mechanics. The same is true of nuclear and particle physics, although an understanding of very high-energy phenomena requires an extension of the theory to include relativistic effects and field quantization, which are briefly discussed in chapter 11. The wavefunction We now discuss the significance of

exp(−κa) (2.40) where (2.37) is obtained by adding (2.33) and (2.35), (2.38) is obtained by subtracting (2.34) from (2.36), and (2.39) and (2.40) are derived similarly. If we now divide (2.38) by (2.37) and (2.40) by (2.39) we get and k tan ka = κ k cot ka = −κ unless C = −D unless C = D and and A=0 B =0 (2.41) The two conditions (2.41) must be satisfied simultaneously, so we have two sets of solutions subject to the following conditions: either or k tan ka = κ k cot ka = −κ C=D C = −D

particles transmitted is just the ratio of the probabilities of the particles being in the transmitted and incident beams, which is just |F|2 /|A|2 and can be evaluated directly from (2.51). In nearly all practical cases, the tunnelling probability is quite small, so we can ignore the term in exp(−κb) in the denominator of (2.51). In this case the tunnelling probability becomes |F|2 16κ 2k 2 16E(V0 − E) = 2 exp (−2κb) = exp (−2κb) 2 |A| (κ + k 2 )2 V02 (2.52) 30 The one-dimensional

line are zero, the summation over p in the last line begins at p = 0. As p is just an index of summation, we can re-write it as p and substitute from (3.38) into (3.36): ∞ {a p+2 ( p + 2)( p + 1) − a p [ p( p + 1) − λ ]}v p = 0 p=0 This can be true only if the coefficient of each power of v is zero, so we obtain the recurrence relation a p+2 p( p + 1) − λ = ap ( p + 1)( p + 2) →1 as p → ∞ (3.39) Separation in spherical polar coordinates 49 Thus, for large p the series (3.37) is identical

corresponding wavefunctions u n are such that, when the operator Hˆ operates on u n , it produces a result equivalent to multiplying u n The dynamical variables 63 by the constant E n . The quantities E n and the functions u n are known as the eigenvalues and eigenfunctions respectively of the operator Hˆ , and we say that the energy of the quantum-mechanical system is represented by an operator Hˆ whose eigenvalues are equal to the allowed values of the energy of the system. For historical

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