Download Fundamentals of Quantum Mechanics: For Solid State by C. L. Tang PDF

By C. L. Tang

Quantum mechanics has advanced from a topic of research in natural physics to 1 with quite a lot of functions in lots of various fields. the elemental strategies of quantum mechanics are defined during this booklet in a concise and easy-to-read demeanour, best towards functions in solid-state electronics and optics. Following a logical series, the ebook makes a speciality of key rules and is conceptually and mathematically self-contained. the basic ideas of quantum mechanics are illustrated by means of displaying their program to structures resembling the hydrogen atom, multi-electron ions and atoms, the formation of easy natural molecules and crystalline solids of useful significance. It leads on from those easy suggestions to debate probably the most major functions in semiconductor electronics and optics. Containing many homework difficulties, the publication is appropriate for senior-level undergraduate and graduate-level scholars in electric engineering, fabric sciences, utilized physics and chemistry.

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2), is a most important basic boundary condition on all wave functions in quantum mechanics. Consider now the boundary condition on the spatial derivative of the wave func@ tion, @x YE ðxÞ. Since the wave function must satisfy the time-independent Schro¨dinger equation, we can integrate it over an infinitesimal range  across the boundary from x ¼ À  / 2 to + / 2:  Zþ2  ! x¼þ2 ! 1 ¼ E À V> YE ðx ¼ 0Þ : 2 x¼À 2 In the limit of  ! 0, one has the boundary condition: ! 1 @ ðIÞ 1 @ ðIIÞ Y ðxÞ Y ðxÞ ¼ : mI @x E mII @x E x¼0 x¼0 (4:3) Since an arbitrary wave function can always be expanded as a superposition of the P i eigen functions of the Hamiltonian, Yðx; tÞ ¼ n Cn YEn ðxÞeÀ"hEn t , the corresponding derivatives of any linear combination of the eigen functions must satisfy the same condition, or: !

4), for example: Yð~ r; t ¼ 0Þ ¼ am YEm ð~ rÞ þ an YEn ð~ rÞ; at some time t later, the state function becomes: i i Yð~ r; tÞ ¼ am YEm ð~ rÞeÀ"hEm t þ an YEn ð~ rÞeÀ"hEn t : (2:22) The corresponding probability distribution function is: i r; tÞj2 ¼ jam YEm ð~ r Þj2 þjan YEn ð~ rÞj2 þaÃm an YÃEm YEn eÀ"hðEn ÀEm Þt jYð~ i þ am aÃn YEm YÃEn e"hðEn ÀEm Þt : (2:23) It contains time-varying terms oscillating at the angular frequency, omn ¼ ðEm À En Þ="h, and is, therefore, ‘‘not stationary’’ in time.

The expansion coefficient Cn has a very simple physical interpretation. Its magnitude squared jCn j2 is the relative probability that measurement of the energy of the system will yield the value En. The absolute probability is P P then jCn j2 = i jCi j2 . If the state function is normalized, or i jCi j2 ¼ 1, then the value of jCn j2 is the absolute probability. 28), the square of the expansion are the eigen functions of the operator Q coefficient Ci gives the probability that measurement of the property Q gives the value qi.

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