Unformatted text preview: in the form ¯ ψ 1 = α ( ψ 1 − εψ 2 ) ¯ ψ 2 = α ( ψ 2 − εψ 1 ) . ±or normalized ψ 1 and ψ 2 the CauchySchwartz inequality says that a ψ 1  ψ 2 A will be less than one. If the states do not overlap much, it will be much less than one and ε will be small. (If ψ 1 and ψ 2 do not meet the stated requirements, you can always rede²ne them by factors ae i c and be − i c , with a , b , and c real, to get states that do.) Answer: The inner product of ¯ ψ 1 and ¯ ψ 2 must be zero for them to be orthogonal: α 2 a ψ 1 − εψ 2  ψ 2 − εψ 1 A = 0...
View
Full Document
 Fall '11
 Dr.DanielArenas
 mechanics, Atom, Molecule, Ion, Hilbert space, Hölder's inequality

Click to edit the document details