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8.5 (a) Apply the Onsager's quantization condition (8.39) to the orbits of free electron levels and show that it leads directly to the free electron levels (8.26) if y= 1/2. (b) Derive an expression for the degeneracy of Landau levels in the case of a two- dimensional free electron gas. Show that the degeneracy is equal to the number of zero-field free electron levels with a given k₂, and with k, and k, within a planar region of area AS given by (8.29). 8.6 An electron in sodium at the Fermi level moves initially in the xy-plane. Calculate the radius of its cyclotron orbit when a magnetic field of 1 T is applied. What is the ratio of the orbit area in real space to that in k-space?

8.5 (a) Apply the Onsager's quantization condition (8.39) to the orbits of free electron levels and show that it leads directly to the free electron levels (8.26) if y= 1/2. (b) Derive an expression for the degeneracy of Landau levels in the case of a two- dimensional free electron gas. Show that the degeneracy is equal to the number of zero-field free electron levels with a given k₂, and with k, and k, within a planar region of area AS given by (8.29). 8.6 An electron in sodium at the Fermi level moves initially in the xy-plane. Calculate the radius of its cyclotron orbit when a magnetic field of 1 T is applied. What is the ratio of the orbit area in real space to that in k-space?

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Please answer 8.5 (a) and (b) 

resonance is observable. 8.5 (a) Apply the Onsager's quantization condition (8.39) to the orbits of free electron levels and show that it leads directly to the free electron levels (8.26) if y = 1/2. (b) Derive an expression for the degeneracy of Landau levels in the case of a two- dimensional free electron gas. Show that the degeneracy is equal to the number of zero-field free electron levels with a given k., and with k, and k, within a planar region of area AS given by (8.29). 8.6 An electron in sodium at the Fermi level moves initially in the xy-plane. Calculate the radius of its cyclotron orbit when a magnetic field of 1 T is applied. What is the ratio of the orbit area in real space to that in k-space?
Transcribed Image Text:resonance is observable. 8.5 (a) Apply the Onsager's quantization condition (8.39) to the orbits of free electron levels and show that it leads directly to the free electron levels (8.26) if y = 1/2. (b) Derive an expression for the degeneracy of Landau levels in the case of a two- dimensional free electron gas. Show that the degeneracy is equal to the number of zero-field free electron levels with a given k., and with k, and k, within a planar region of area AS given by (8.29). 8.6 An electron in sodium at the Fermi level moves initially in the xy-plane. Calculate the radius of its cyclotron orbit when a magnetic field of 1 T is applied. What is the ratio of the orbit area in real space to that in k-space?
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