Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 6, Problem 6Q
To determine
Whether the statement
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Complete the derivation of E =
Taking the derivatives we find (Use the following as necessary: k₁, K₂ K3, and 4.)
+- ( ²) (²)
v² =
SO
- #2² -
=
2m
so the Schrödinger equation becomes (Use the following as necessary: K₁, K₂, K3, ħ, m and p.)
亢
2mm(K² +K ² + K² v
k₁ =
E =
= EU
The quantum numbers n, are related to k, by (Use the following as necessary: n, and L₁.)
лħ n₂
π²h²
2m
√2m
h²²/0₁
2m
X
+
+
by substituting the wave function (x, y, z) = A sin(kx) sin(k₂y) sin(kz) into -
13³3).
X
What is the origin of the three quantum numbers?
O the Schrödinger equation
O the Pauli exclusion principle
O the uncertainty principle
Ⓒthe three boundary conditions
2² 7²4 = E4.
2m
Consider the electron in a hydrogen atom is in a state of ψ(r) = (x + y + 3z)f(r).where f(r) is an unknown function depending only on r.(a) Is ψ an eigenstate of Lˆ2? Find the eigenvalue if your answer is ’Yes’.(b) Compute the probabilities of finding this electron in eigen states with m = −1, 0, +1. (c) Compute <Lz> in this state.
A spherical harmonic function is the angular part of the wavefunction of an electron in
hydrogen atom.
In the state (5,4,-2), it is the following,
Y, (0, ø) =V exp[-2iø] sin? 0 (7 cos² 0 – 1)
A. What is the most probable angle 0 to find the electron?
If there are more than one angle, please enter one of the correct answers.
Answer:
Chapter 6 Solutions
Modern Physics
Ch. 6.4 - Prob. 1ECh. 6.4 - Prob. 2ECh. 6.5 - Prob. 4ECh. 6.7 - Prob. 5ECh. 6.8 - Prob. 6ECh. 6 - Prob. 1QCh. 6 - Prob. 2QCh. 6 - Prob. 3QCh. 6 - Prob. 4QCh. 6 - Prob. 5Q
Ch. 6 - Prob. 6QCh. 6 - Prob. 7QCh. 6 - Prob. 8QCh. 6 - Prob. 1PCh. 6 - Prob. 2PCh. 6 - Prob. 3PCh. 6 - Prob. 5PCh. 6 - Prob. 6PCh. 6 - Prob. 7PCh. 6 - Prob. 8PCh. 6 - Prob. 9PCh. 6 - Prob. 10PCh. 6 - Prob. 11PCh. 6 - Prob. 12PCh. 6 - Prob. 13PCh. 6 - Prob. 14PCh. 6 - Prob. 15PCh. 6 - Prob. 16PCh. 6 - Prob. 17PCh. 6 - Prob. 18PCh. 6 - Prob. 19PCh. 6 - Prob. 21PCh. 6 - Prob. 24PCh. 6 - Prob. 25PCh. 6 - Prob. 26PCh. 6 - Prob. 28PCh. 6 - Prob. 29PCh. 6 - Prob. 30PCh. 6 - Prob. 31PCh. 6 - Prob. 32PCh. 6 - Prob. 33PCh. 6 - Prob. 34PCh. 6 - Prob. 35PCh. 6 - Prob. 37PCh. 6 - Prob. 38P
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