Podcast
Questions and Answers
What is the value of the commutator [A, B^2] given that [A, B] = 1?
What is the value of the commutator [A, B^2] given that [A, B] = 1?
Which of the following statements about the hermitian nature of operators is correct?
Which of the following statements about the hermitian nature of operators is correct?
What is the expectation value of the momentum px for a particle confined in a one-dimensional box with zero potential energy?
What is the expectation value of the momentum px for a particle confined in a one-dimensional box with zero potential energy?
If the normalized wavefunction for a particle in a box is $Ψ_n(x) = (2/a)^{1/2} sin(nπx/a)$, which of the following statements is true regarding its properties?
If the normalized wavefunction for a particle in a box is $Ψ_n(x) = (2/a)^{1/2} sin(nπx/a)$, which of the following statements is true regarding its properties?
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What is the primary purpose of evaluating the value of the commutator [, [, A]]?
What is the primary purpose of evaluating the value of the commutator [, [, A]]?
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Study Notes
Course Overview
- Course Title: Physical Chemistry-I
- Course Code: CHCHC03
- Degree: M.Sc.
- Semester: 1st
- Total Pages: 1
- Exam Duration: 1 hour and 30 minutes
Examination Instructions
- All questions must be attempted.
- Missing data can be assumed as necessary.
Questions Breakdown
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Question 1(a): Involves operators ( A ) and ( B ) with a commutation relation ( [A, B] = 1 ). Task is to find ( [A, B^2] ) (2 marks).
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Question 1(b):
- Statements assessed for hermitian nature:
- ( (A + A^*) ) is hermitian.
- ( i(A + A^*) ) is hermitian.
- Additional inquiry: Is ( A = -\frac{d}{dx} + x ) hermitian? (2 marks + 1 mark for justification).
- Statements assessed for hermitian nature:
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Question 2(a): Evaluate the value of the commutator ( [, [, A]] ) (2 marks).
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Question 2(b):
- Calculate the expectation values of position ( x ) and momentum ( p_x ) for a particle in a one-dimensional box of width ( a ).
- Given normalized wavefunction:
[ Ψ_n(x) = \left(\frac{2}{a}\right)^{1/2} \sin\left(\frac{n\pi x}{a}\right) ] (3 marks).
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Question 3(a): Computes the probability of finding an electron in a 1-D box of specified length (exact length not provided).
Key Concepts
- Operators & Commutation Relations: Fundamental in quantum mechanics for understanding how physical quantities relate to each other.
- Hermitian Operators: Critical for defining observable quantities; have real eigenvalues.
- Expectation Values: Describes average outcomes in quantum states, crucial for predicting measurement results in quantum systems.
- Wavefunction Normalization: Ensures probabilities derived from the wavefunction sum to 1, enabling physical interpretation.
Additional Notes
- Ensure to understand and apply the principles of quantum mechanics related to operators, eigenvalues, and wavefunctions.
- Utilize mathematical proofs and justifications effectively when answering theoretical questions.
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Description
This quiz assesses knowledge from the M.Sc. Physical Chemistry-I course, focusing on operator theory and related problems. Students are required to answer all questions, demonstrating their understanding of fundamental concepts and calculations in physical chemistry.
