Condensed Matter equations + more

Question 1

What gives the distance between two lattice planes in terms of the orthogonal k-space lattice vector?

Answer 1

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Question 2

What should we use as our ansatz for the lattice point coefficient in tight-binding problems?

Answer 2

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Question 3

What is the relation between the incoming and outgoing k-vector from bragg scattering?

Answer 3

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Question 4

What is the bragg condition?

Answer 4

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Question 5

What is the form of a tight-binding equation?

Answer 5

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Question 6

What integral do we use for the number of occupied states in a system?

Answer 6

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Question 7

What gives the fermi and bose distributions for 0 chemical potential?

Answer 7

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Question 8

What is an equation for the effective mass of an electron in a lattice potential?

Answer 8

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Question 9

What gives the cyclotron frequency for a 2D sqaure lattice?

Answer 9

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Question 10

What is the partition function?

Answer 10

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Question 11

How do we extract the free energy from the partition function?

Answer 11

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Question 12

How do we extract the magnetisation from the free energy?

Answer 12

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Question 13

How do we extract the susceptibility from the magnetisation?

Answer 13

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Question 14

What is an equation for the magnetisation given no exchange term?

Answer 14

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Question 15

What is a form of the effective magnetic field in the mean-field approximation?

Answer 15

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Question 16

What are the double angle formulae?

Answer 16

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Question 17

How do the trig expansions relate to the hyperbolic ones?

Answer 17

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Question 18

What is the fermi wavevector for a 3D solid with non-relativistic electrons?

Answer 18

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