Quantum Mechanics I [IAS (Admin.) Mains Physics]: Questions 1 - 6 of 50

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Question 1

Appeared in Year: 2011 (IFS)

Describe in Detail Subjective▾

On the basis of uncertainty principle calculate the size of Hydrogen atom.

(Paper-2) (Section - A)

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Explanation

  • From a hydrogen atom, it is not possible to predict exact the position of the electron or the momentum of the electron. Every time the electron is at somewhere but it has amplitude to in different places so there is a probability of it being found in different places.
  • These places cannot all be at the nucleus; we shall suppose there is a spread in p…

… (225 more equations) …

Question 2

Appeared in Year: 2011 (IFS)

Describe in Detail Subjective▾

Solve the Schrodinger equation for a potential step function given by,

and calculate the reflection and transmission coefficients. Show that for there is a finite probability of finding the particle in a classically forbidden region.

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Explanation

  • Consider . The time independent Schrodinger equation in one dimension is given as,

… (543 more equations, 10 figures) …

Question 3

Appeared in Year: 2011 (IFS)

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For a quantum mechanical system prove that all energy eigen – values are real and if , then the corresponding eigen functions are orthogonal.

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Explanation

  • The eigenvalue equation, of the sets of energies and wave functions obtained by any quantum mechanics problems is given as,

    For another value of the quantum number, we can write

… (116 more equations) …

Question 4

Appeared in Year: 2011

Describe in Detail Subjective▾

Solve the Schrodinger equation for a particle of mass m in an infinite rectangular well defined by the potential

Obtain the normalized Eigen function and the corresponding Eigen values. (25 Marks)

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Explanation

The One-Dimensional Time Independent Schrodinger Equation
  • The one-dimensional time independent Schrodinger equation of the particle inside the well where , is

… (364 more equations, 16 figures) …

Question 5

Appeared in Year: 2011

Describe in Detail Subjective▾

Calculate (15 Marks)

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Explanation

… (379 more equations) …

Question 6

Appeared in Year: 2007

Describe in Detail Subjective▾

Solve the Schrodinger equation for a linear harmonic oscillator obtain the eigen values and the corresponding Eigen functions. (40 Marks)

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Explanation

  • The Schrodinger equation for harmonic oscillator is

    … eq. (1)

  • And solve it directly by the series method. Let us introduc…

… (1400 more equations) …