Give short answers for the following questions: 1. Concerning with the probability density, what is the major assumption of WKB method? 2. Write the assumption that made the rough-... Give short answers for the following questions: 1. Concerning with the probability density, what is the major assumption of WKB method? 2. Write the assumption that made the rough-treatment conform to the first-order correction of the formal treatment. 3. State the occasions for using time independent degenerate perturbation theory. 4. What is the meaning of minimization in the variation method? 5. State the physical meaning of plus and minus signs that appear in the following two formulas; Ψ200 = 2^{1/2}(1200) + 2^{1/2}(210) and Ψ210 = 2^{1/2}(200) - 2^{1/2}(210).
Understand the Problem
The question is asking for short answers to a series of concepts related to quantum mechanics, specifically the WKB method, perturbation theory, and variational methods, requiring explanations or definitions based on these topics.
Answer
1. Slow potential variation. 2. Higher order terms negligible. 3. Degenerate energy levels. 4. Lowest energy state. 5. Interference in superposition.
- The major assumption of the WKB method is that the potential varies slowly in comparison to the wavelength.
- The assumption is that higher order terms are negligible, making the rough-treatment valid for first-order correction.
- Time independent degenerate perturbation theory is used when dealing with systems that have degenerate energy levels.
- In the variation method, minimization refers to finding the lowest energy state by varying the trial wavefunction.
- The plus and minus signs correspond to constructive and destructive interference in quantum superposition.
Answer for screen readers
- The major assumption of the WKB method is that the potential varies slowly in comparison to the wavelength.
- The assumption is that higher order terms are negligible, making the rough-treatment valid for first-order correction.
- Time independent degenerate perturbation theory is used when dealing with systems that have degenerate energy levels.
- In the variation method, minimization refers to finding the lowest energy state by varying the trial wavefunction.
- The plus and minus signs correspond to constructive and destructive interference in quantum superposition.
More Information
The WKB method is often used for quantum systems with slowly varying potentials, making it a crucial tool in quantum mechanics. The variation method helps find the ground state energy efficiently.
Tips
In WKB problems, ensure potential variation is considered correctly. For variation methods, a proper choice of trial wavefunction is critical.
Sources
- WKB approximation - Wikipedia - en.wikipedia.org
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