Oscillator variationally.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
please answer in a clear way and show explicitly what you are computing. do not skip any steps
Transcribed Image Text:Use a trial function (x)=1/(1+Bx²)² to calculate the ground-state energy of a harmonic
oscillator variationally.
Hints: The necessary integrals are
And
dx
(2n-3)(2n- 5)(2n-7)....(1) π
[_x (+3x²)"
> (1+ßx²)"¯¯¯ (2n − 2)(2n— 4)(2n – 6)....(2) 3¹/²
x² dx
∞ (1+Bx²)"
fo
=
(2n- 5)(2n-7)(2n-9)....(1) π
(2n-2)(2n-4)(2n-6)....(2) 33/2
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