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| courses:ast301:2 [2024/03/15 02:25] – asad | courses:ast301:2 [2024/03/15 02:26] (current) – [3.1 Degeneracy in 1D] asad | ||
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| To explain degeneracy, consider a gas of 37 electrons occupying the states shown in the 1D phase-space diagram of Fig. (a) following MBS. They are not degenerate. Most of them are occupying the lowest states as dictated by 1D MBD. The momentum at which kientic energy is equal to $E_{av}=kT/ | To explain degeneracy, consider a gas of 37 electrons occupying the states shown in the 1D phase-space diagram of Fig. (a) following MBS. They are not degenerate. Most of them are occupying the lowest states as dictated by 1D MBD. The momentum at which kientic energy is equal to $E_{av}=kT/ | ||
| - | If this gas loses energy and cools down, the electrons will lose energy and settle down at the bottom of the diagram as in Fig. (c). All the low states are completely filled. Many of the electrons thus have a higher energy than they would normally have at this low temperature. This unusually higher energy creates the degeneracy pressure. The momentum at the upper end of the FDD is called the Fermi momentum $p_F$. The FD distribution $P(p_x)$ looks almost rectangular, | + | If this gas loses energy and cools down, the electrons will lose energy and settle down at the bottom of the diagram as in Fig. (C). All the low states are completely filled. Many of the electrons thus have a higher energy than they would normally have at this low temperature. This unusually higher energy creates the degeneracy pressure. The momentum at the upper end of the FDD is called the Fermi momentum $p_F$. The FD distribution $\mathsf{P}(p_x)$ looks almost rectangular, |
| We can make a gas degenerate by squeezing it (decreasing $\Delta X$) instead of cooling, i. e. by moving from Fig. (a) to (b). Moving from (b) to (d) we see that the electrons remain almost in the same states. That means in a completely degenerate gas, the pressure becomes independent of temperature. | We can make a gas degenerate by squeezing it (decreasing $\Delta X$) instead of cooling, i. e. by moving from Fig. (a) to (b). Moving from (b) to (d) we see that the electrons remain almost in the same states. That means in a completely degenerate gas, the pressure becomes independent of temperature. | ||
courses/ast301/2.1710491117.txt.gz · Last modified: 2024/03/15 02:25 by asad