(1|H|2) = (yo (x) yo (y) yı (z) |λx²yz|yo (x) yı (y) yo (z)) (x²) (0 [y] 1) (1 [z] 0) = ^ 2m (0 [x] = 2 ( 7 1)/² |x|1)|² 2 ħ 2mw
(1|H|2) = (yo (x) yo (y) yı (z) |λx²yz|yo (x) yı (y) yo (z)) (x²) (0 [y] 1) (1 [z] 0) = ^ 2m (0 [x] = 2 ( 7 1)/² |x|1)|² 2 ħ 2mw
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This is the solution to problem 7.36 . Could you explain the yellow marked place ? How we got <0|y|1> and <x^2>0 ?
Transcribed Image Text:Problem 7.36 Consider the isotropic three-dimensional harmonic oscillator
(Problem 4.46). Discuss the effect (in first order) of the perturbation
H' = λx²yz
(for some constant λ) on
(a) the ground state;
(b)
the (triply degenerate) first excited state. Hint: Use the answers to
Problems 2.12 and 3.39.
![Introduction To Quan... 3rd Edition
= 2(x²)o(y)o(z)₁
= 0
(2|H|2) = (yo (x) y (v) yo (z) x²yzo (x) yn (v) yo (2))
= 2(x²)o(v)₁ (²)0
= 0
(3|H|3) = (y₁ (x) yo (y) yo (z) |λx²yz|y₁ (x) yo (y) yo (z))
= 2(x²), (v)o(z)o
= 0
Using Problem 2.11 and 3.39,
(1|H|2) = (yo (x) yo (y) yı (z) |λx²yz|yo (x) yı (y) yo (z))
(x²) (0 [v] 1) (1 [z] 0)
WE
ħ
= 2:
AKO |x|1)|²
2mw
(1|H|2) = (yo (x) yo (y) yn (z) |λx²yz|yn (x) yo (v) yo (z))
= 2 (0x²| 1) (y)o (1|2|0)
= 0
ħ 2
= A ( 2 m ) ²
(2|H|3) = (yo (x) yn (v) yo (2) ix²yzyn (x) yo (v) yo (z))
= 2 (0|x²| 1) (1 ly 0) (z)o
0
TALK](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F27881e66-694c-4814-b35a-fba75a4bbb38%2Fb94a7684-1ff1-4186-a891-0313528b3ce2%2Feseaxj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Introduction To Quan... 3rd Edition
= 2(x²)o(y)o(z)₁
= 0
(2|H|2) = (yo (x) y (v) yo (z) x²yzo (x) yn (v) yo (2))
= 2(x²)o(v)₁ (²)0
= 0
(3|H|3) = (y₁ (x) yo (y) yo (z) |λx²yz|y₁ (x) yo (y) yo (z))
= 2(x²), (v)o(z)o
= 0
Using Problem 2.11 and 3.39,
(1|H|2) = (yo (x) yo (y) yı (z) |λx²yz|yo (x) yı (y) yo (z))
(x²) (0 [v] 1) (1 [z] 0)
WE
ħ
= 2:
AKO |x|1)|²
2mw
(1|H|2) = (yo (x) yo (y) yn (z) |λx²yz|yn (x) yo (v) yo (z))
= 2 (0x²| 1) (y)o (1|2|0)
= 0
ħ 2
= A ( 2 m ) ²
(2|H|3) = (yo (x) yn (v) yo (2) ix²yzyn (x) yo (v) yo (z))
= 2 (0|x²| 1) (1 ly 0) (z)o
0
TALK
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