Numerical Solution of Harmonic Oscillator

d2 Ψ(x) − 2 + x2 Ψ(x) = 2E Ψ( dx

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H x = λx

Y k = (A − αI )−1 X k X k+1 =

Y k ||Y k || α X 0

10−8

2E n = 2(n + 12 ) = 1, 3, 5,...

−10 ≤ x ≤ 10

N  = 100 x = −10 + h

x = 10 − h tol = 10−8

λnum λana λnum n = 60

λana

40 ≤ n ≤ 50

O · OT  = I d

||res|| = ||λnum · xi − H  · xi || i ||res||

||res||