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
Describe in Detail
On the basis of uncertainty principle calculate the size of Hydrogen atom.
(Paper2) (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 places cannot all be at the nucleus; we shall suppose there is a spread i…
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Question number: 2
» Quantum Mechanics I » Particle in a Finite Well, Linear, Harmonic Oscillator, Reflection
Appeared in Year: 2011
Describe in Detail
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.
Explanation

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

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

Let the region of negative is denoted by and region of positive is denoted by . Also corresponding wave functions and , respectively.

From given conditions, Schrodinger equation…
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Question number: 3
» Quantum Mechanics I » Schroedinger Equation and Expectation Values
Appeared in Year: 2011
Describe in Detail
For a quantum mechanical system prove that all energy eigen – values are real and if , 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,
For another value of the quantum number, we can write

Multiply equation (1) by and the complex conjugate of equation (2) by . Then subtract the two expressions and integrate over .

The left hand side of equatio…
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