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A particle of mass m is confined in an infinite square well with a shelf of height V0 extending half way across so that :

Using WKB approximation, the allowed energies En (n = 1, 2, 3,....) for this particle are, (given are the energies of particle in an infinite well with no shelf) :
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A particle of mass m is confined in an infinite square well with a she...
The Schrodinger equation is given by 
The above equation can be written as where 
Now, we know that is the value for any wavefunction.
So, the solution of above equation using WKB Approximation, is 
Calculation:



We are finding the energies of the particle from a to-a in an infinite potential well.
Using WKB Approximation, is 
Now, we will substitute value of p(x) in above integration equation and taking limits from 0 to a and a to a/2 and V = V0 for first term and  V = 0 for second term, we get then,

After integration with respect to x, and applying limits, we get,


Taking andto right hand side, we get, 


Squaring both sides, and putting 


Take term αn to left side, we get,

Again squaring both sides, we get,

Cancelling terms and find the value of E, we get,


Now, substitute value of in above equation, we get,



So, the correct answer is 
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A particle of mass m is confined in an infinite square well with a shelf of height V0 extending half way across so that :Using WKB approximation, the allowed energies En (n = 1, 2, 3,....) for this particle are, (givenare the energies of particle in an infinite well with no shelf) :a)b)c)d)Correct answer is option 'D'. Can you explain this answer?
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A particle of mass m is confined in an infinite square well with a shelf of height V0 extending half way across so that :Using WKB approximation, the allowed energies En (n = 1, 2, 3,....) for this particle are, (givenare the energies of particle in an infinite well with no shelf) :a)b)c)d)Correct answer is option 'D'. 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 of mass m is confined in an infinite square well with a shelf of height V0 extending half way across so that :Using WKB approximation, the allowed energies En (n = 1, 2, 3,....) for this particle are, (givenare the energies of particle in an infinite well with no shelf) :a)b)c)d)Correct answer is option 'D'. 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 of mass m is confined in an infinite square well with a shelf of height V0 extending half way across so that :Using WKB approximation, the allowed energies En (n = 1, 2, 3,....) for this particle are, (givenare the energies of particle in an infinite well with no shelf) :a)b)c)d)Correct answer is option 'D'. Can you explain this answer?.
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