REQUIRED Consider the one dimensional harmonic oscillator. (a) Prove that (b) Prove that (c) Prove that (d) Prove that for any eigenstate [n). [a, a¹] = 1. H = ħw (a¹a + 2 H|n) = ħw (n + ¹) |n). 2 (n|T|n) = (n|V|n)
REQUIRED Consider the one dimensional harmonic oscillator. (a) Prove that (b) Prove that (c) Prove that (d) Prove that for any eigenstate [n). [a, a¹] = 1. H = ħw (a¹a + 2 H|n) = ħw (n + ¹) |n). 2 (n|T|n) = (n|V|n)
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![9. REQUIRED Consider the one dimensional harmonic oscillator.
(a) Prove that
(b) Prove that
(c) Prove that
(d) Prove that
for any eigenstate [n).
H
[a, a¹] = 1.
=
(a²a + 1/2)
(n + 1 ² ) In).
H|n) = ħw (n +
(n|T|n) = (n|V|n)
(8)
(9)
(10)
(11)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53063809-76ad-4290-96f6-51248e3ef27e%2F3c678b83-24ff-4430-ad23-4dbaebe17a01%2Famugh38_processed.jpeg&w=3840&q=75)
Transcribed Image Text:9. REQUIRED Consider the one dimensional harmonic oscillator.
(a) Prove that
(b) Prove that
(c) Prove that
(d) Prove that
for any eigenstate [n).
H
[a, a¹] = 1.
=
(a²a + 1/2)
(n + 1 ² ) In).
H|n) = ħw (n +
(n|T|n) = (n|V|n)
(8)
(9)
(10)
(11)
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