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A particle in 1-D moves under the influence of a potential of V(x) a x4, where a is a real constant. For large the quantized energy En depends on as:
  • a)
    E∝n4/3
  • b)
    E∝n3/4
  • c)
     
    E∝n2/3
  • d)
    E∝n3/2
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A particle in 1-D moves under the influence of a potential of V(x) a x...
According to WKB approximation:
We have to use the relation that:

where,for V (x) to be finite a boundary andfor V(x) to be infinite at the boundary.
Explanation:
We have a particle in 1-D that moves under the influence of a potential of V(x) a x4.
We use the above formula with as the potential is finite at the turning points, and we get:

The potential is symmetric hence,
where A is some constant
Taking the substitution we get:

Now pulling out all the E terms, out and doing the integration we get:
This constant carries a constant after doing the integration.
Now solving it a bit we get:

Therefore:
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A particle in 1-D moves under the influence of a potential of V(x) a x4, where a is a real constant. For largenthe quantized energy Endepends onnas:a)E∝n4/3b)E∝n3/4c)E∝n2/3d)E∝n3/2Correct answer is option 'A'. Can you explain this answer?
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A particle in 1-D moves under the influence of a potential of V(x) a x4, where a is a real constant. For largenthe quantized energy Endepends onnas:a)E∝n4/3b)E∝n3/4c)E∝n2/3d)E∝n3/2Correct answer is option 'A'. Can you explain this answer? for UGC NET 2024 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about A particle in 1-D moves under the influence of a potential of V(x) a x4, where a is a real constant. For largenthe quantized energy Endepends onnas:a)E∝n4/3b)E∝n3/4c)E∝n2/3d)E∝n3/2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for UGC NET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle in 1-D moves under the influence of a potential of V(x) a x4, where a is a real constant. For largenthe quantized energy Endepends onnas:a)E∝n4/3b)E∝n3/4c)E∝n2/3d)E∝n3/2Correct answer is option 'A'. Can you explain this answer?.
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