Chapter 12 (III)

Chapter 12 (III) - 12.6 Energy Levels and Quantum States )....

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Unformatted text preview: 12.6 Energy Levels and Quantum States ). , ( ) , ( t r t r H j r r = In quantum mechanics, the N-particle system contained in a finite volume may exist in any one of an enormous number of discrete states determined by the Schrdinger equation Each energy eigen value j corresponds to one or more quantum states described by the wave function , that is, there may be many quantum states having the same energy. These states are called to be degenerate. The number of quantum states at an energy level j is called the degeneracy g j . ) , ( t r r Consider a simplest case in quantum mechanics: a particle of mass m in an one-dimensional box with infinitely high walls. In this case, the wave function is: The probability of finding the particle at a position x in the box is determined by (x) = Asinkx (0 x L), and (0)= (L)=0. With the wavenumber k by n=1, 2, 3, . ) ( ) , ( / h r t i e x t r = x=0 x=L V= V= , L n k = This is analogous to the vibrational wave of a string with both ends fixed: (x) = Asin(2 x/ ), where k= 2 / ....
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Chapter 12 (III) - 12.6 Energy Levels and Quantum States )....

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