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2. The quantum states of a particle moving freely in a circle of radius r are described by Vn(0) = Ceno 0, ±1, +2, ... is an integer identifying where C is a constant, 0 denotes angle, n the quantum state of the particle, and wn is constant for a given n. a) Show that bn(0) satisfies d02 b) Find wn such that n(0 + 27) = n(0) c) Find the value of C such that I lein(0)|²d® = 1 %3D

2. The quantum states of a particle moving freely in a circle of radius r are described by Vn(0) = Ceno 0, ±1, +2, ... is an integer identifying where C is a constant, 0 denotes angle, n the quantum state of the particle, and wn is constant for a given n. a) Show that bn(0) satisfies d02 b) Find wn such that n(0 + 27) = n(0) c) Find the value of C such that I lein(0)|²d® = 1 %3D

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter28: Quantum Physics
Section: Chapter Questions
Problem 6CQ
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Answer d step by step. Please explain how you integrate complex exponentials

2. The quantum states of a particle moving freely in a circle of radius r are described by bn (0) C'ewno where C is a constant, 0 denotes angle, n = 0, ±1,±2, ... is an integer identifying the quantum state of the particle, and wn is constant for a given n. a) Show that ,(0) satisfies d02 b) Find w, such that Wn(0 +27) = n(0) c) Find the value of C such that 27T | In (0)l°d0 = 1 d) Show that any two v,(0) and m(0) with m +n satisfy | (0)bm (0)d0 = 0
Transcribed Image Text:2. The quantum states of a particle moving freely in a circle of radius r are described by bn (0) C'ewno where C is a constant, 0 denotes angle, n = 0, ±1,±2, ... is an integer identifying the quantum state of the particle, and wn is constant for a given n. a) Show that ,(0) satisfies d02 b) Find w, such that Wn(0 +27) = n(0) c) Find the value of C such that 27T | In (0)l°d0 = 1 d) Show that any two v,(0) and m(0) with m +n satisfy | (0)bm (0)d0 = 0
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