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Chapter6_19

# Chapter6_19 - PHY3063 R D Field Theory of Stationary...

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PHY3063 R. D. Field Department of Physics Chapter6_19.doc University of Florida Theory of Stationary States (2) Probability Density: The probability density, in general, depends on time and is given by ∑ ∑ = = = + = Ψ Ψ = 1 1 1 ) , ( ) , ( ) , ( m t i m n n n m n m n n n n n mn e c c c c t x t x t x ω ψ ψ ψ ψ ρ where h / ) ( n m mn E E = ω and called the “transition” frequencies. Average Energy: The average energy of the arbitrary state = = = Ψ = Ψ 1 / 1 ) ( ) , ( ) , ( n t iE n n n n n n e x c t x c t x h ψ . is = = = >= < 1 2 1 | | n n n n n n n E c E c c E and P n = |c n | 2 is the probability that in a single measurement of the energy of the arbitrary state Ψ one would find E n . Proof: ∑ ∑ = = = = = > < + > < >= Ψ Ψ >=< < 1 * 1 / ) ( 1 * 1 * | | | | n n n n m t E E i j m n n i n n m n n n n n n op E c c e E c c E c c H E m n h ψ ψ ψ ψ Overlap Functions:
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