GATE CY Structure PYQs & Answers — Page 4

Questions 31–40 of 46. Imported answers require independent review unless marked reviewed.

Topic practice 46 questionsPage 4 of 5

The % error (rounded off to two decimal places) in the ground state energy of a particle in a one dimensional box of length ‘a’ described by a trial variation function

, where

, is ______

(Given: The true ground state energy of the above system is

;

)

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Suppose the wave function of a one dimensional system is

. In an experiment measuring the momentum of the system, one of the expected outcomes is

Your answerChoose one option.

ℏk

2 ℏk

3 ℏk

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, where

and

are spin angular momentum operators and

is spin up eigen function, then the value of ‘a’ is ________. (Round off to one decimal place)

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A particle in one dimensional box of length

with potential energy

is perturbed by the potential

eV, where

is a constant. The 1st order correction to the 1st excited state of the system is __________ ×

eV.

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Consider a two dimensional harmonic oscillator with angular frequency

. The wavelength of x polarized light required for the excitation of a particle from its ground state to the next allowed excited state is ________ ×

m. (Round off to one decimal place)

(Speed of light

)

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The spherical harmonic function,

, with appropriate values of l and m, is an eigenfunction of

operator. The corresponding eigenvalue is

Your answerChoose one option.

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Consider the operators,

and

, where

and

are the position and linear momentum operators, respectively. The commutator,

, is equal to

Your answerChoose one option.

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The energy of a hydrogen molecule in its ground state equilibrium configuration is −31.7 eV. Its dissociation energy is _________ eV. (Up to one decimal place)

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A one-dimensional anharmonic oscillator is treated by perturbation theory. The harmonic oscillator is used as the unperturbed system and the perturbation is

(

is a constant). Using only the first order correction, the total ground state energy of the anharmonic oscillator is

(Note: For a one-dimensional harmonic oscillator

)

Your answerChoose one option.

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In a molecule XY, let

and

denote normalized atomic orbitals of atoms X and Y, respectively. A normalized molecular orbital of XY is given by

. The value of the overlap integral of

and

is ________________. (Up to two decimal places)

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GATE CY Structure PYQs

Question 50

Question 33

Question 53

Question 54

Question 55

Question 7

Question 8

Question 22

Question 34

Question 48