The ground state energy of a particle of mass m in the potential V(x)={V}_{0}cosh \left( \frac{x}{L} \right), where L and {V}_{0} are constants (with {V}_{0}\gg \frac{{\hbar }^{2}}{2m{l}^{2}}) is approximately

Variational Principle — CSIR Net PYQ (Question 1)

A Variational Principle previous-year question (PYQ) from Quantum Mechanics (CSIR Net). Read the question, check the correct answer, then practise the full topic.

Question 1 of 5 · 3.5 marks

The ground state energy of a particle of mass

m

in the potential

V (x) = V_{0} cos h (\frac{x}{L})

, where

L

and

V_{0}

are constants (with

V_{0} ≫ \frac{ℏ ^{2}}{2 m l ^{2}}

) is approximately

1 $V_{0} + \frac{ℏ}{L} \frac{2 V _{0}}{m}$
2 $V_{0} + \frac{ℏ}{L} \frac{V _{0}}{m}$
3 $V_{0} + \frac{ℏ}{4 L} \frac{V _{0}}{m}$
4 $V_{0} + \frac{ℏ}{2 L} \frac{V _{0}}{m}$

Correct answer: Option 4

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