Unformatted text preview: 1 > and  Ψ 2 > is < Ψ 1  Ψ 2 > like the dot product of two vectors 2 1 V V r r ⋅ < Ψ 1  Ψ 2 > is a complex number The scalar product < Ψ 2  Ψ 1 > is referred to as the “overlap” between the two states. Norm of a State: The “norm” of the “Ketvector”  Ψ > is the scalar product of  Ψ > with itself < Ψ  Ψ > like the square of a vector V V r r ⋅ < Ψ  Ψ > ≥ 0 (positive definite real number) Normalized wavefunctions have < Ψ  Ψ > = 1 and two wavefunctions are said to be “orthogonal” if their overlap is zero, < Ψ 2  Ψ 1 > = 0 . An “orthonormal” set of wavefunctions has the property that ij j i δ >= Ψ Ψ <  . “KetVector” Space:  Ψ i > “BraVector” Space: < Ψ i  Dual (“Adjoint”) Like Ψ (x,t)! Like Ψ ∗ (x,t)!...
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This note was uploaded on 05/29/2011 for the course PHY 3063 taught by Professor Field during the Spring '07 term at University of Florida.
 Spring '07
 Field
 Physics

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