Quantum Mechanics I (IFS (Forests Services) Physics (Mains)): Questions 1 - 3 of 3

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Question number: 1

» Quantum Mechanics I » Uncertainty Principle

Appeared in Year: 2011

Essay Question▾

Describe in Detail

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

(Paper-2) (Section - A)

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
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Question number: 2

» Quantum Mechanics I » Particle in a Finite Well, Linear, Harmonic Oscillator, Reflection

Appeared in Year: 2011

Essay Question▾

Describe in Detail

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

Equation

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

Explanation

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

    Equation

  • And according to question, the potential step function is given as,

    Equation

  • Let the region of negative Equation is denoted by Equation and region of positive Equation is denoted by Equation . Also corresponding wave

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Question number: 3

» Quantum Mechanics I » Schroedinger Equation and Expectation Values

Appeared in Year: 2011

Essay Question▾

Describe in Detail

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

Explanation

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

    Equation

    For another value of the quantum number, we can write

    Equation

  • Multiply equation (1) by Equation and the complex conjugate of equation (2) by Equation . Then subtract the

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