# IFS (Forests Services) Physics (Mains): Questions 26 - 31 of 34

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## Question number: 26

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Appeared in Year: 2011

Essay Question▾

### 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 reg

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## Question number: 27

» Quantum Mechanics II & Atomic Physics » Quantum Mechanics II » The Spin Half Problem and Properties of Pauli Spin Matrices

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Appeared in Year: 2011

Essay Question▾

### Describe in Detail

What are Pauli spin matrices?

Show that:

Where, are Pauli spin matrices and and are vector operators which commute with , but do not necessarily commute with each other?

### Explanation

Pauli spin matrices or Pauli matrices are a set of matrices, which are complex, Hermitian and unitary matrices. Pauli spin matrices defined as,

The Pauli vector is defined by,

From question another vector operators are and ar

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## Question number: 28

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Appeared in Year: 2011

Essay Question▾

### Describe in Detail

Give the elementary theory of NMR. Explain the two different relaxation processes. (Paper – II)

### Explanation

• In Nuclear Magnetic Resonance (NMR), the frequency of processing nucleus is equal to the frequency of rotating magnetic field. Here it is important to notice that in NMR we are not performing experiments on the electron, it all about the nuclei of the nucleus.

• The principle of NMR is dependent on the spins of atomic nuclei. Consider, the subatomic p

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## Question number: 29

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Appeared in Year: 2011

Essay Question▾

### 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 expres

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## Question number: 30

» Particle Physics & Solid State Physics » Solid State Physics » Band Theory of Solids-Conductors

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Appeared in Year: 2011

Essay Question▾

### Describe in Detail

How are the band structures of insulators and semiconductors similar? How are they different?

### Explanation

• There is only one similarity in band structures of insulators and semiconductors. That is band gab between valence band and conduction band. And in case of conductor, there is no such band gap between valence and conduction bands.
• In insulators, the valence band is completely full with elec

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## Question number: 31

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Appeared in Year: 2011

Essay Question▾

### Describe in Detail

What are intrinsic and extrinsic semi – conductors? Explain.

How are type and type semiconductors obtained?

### Explanation

Intrinsic Semiconductors:

• Intrinsic semiconductors are pure semiconducting material and no impurity atoms are added to them. The conductivity of the intrinsic semiconductor are at the room temperature is zero. It means the valence band of the intrinsic semiconductor is completely filled and conduction band is completely empty at room temperature.

• The

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