2) The energy levels of a quantum-mechanical, one-dimensional, anharmonic oscillator maybe approximated as 2 =(n * (n + )' En hw ;n = 0,1,2,... (++) = The parameter x, usually « 1, represents the degree of anharmonicity. Show that, to the first order in x and the fourth order in u (= ħw/kgT), the specific heat of a system of N such oscillators is given by C = Nk [(1-u² + *)+ 4x (: + *)]. 240 80 Note that the correction term here increases with temperature.
2) The energy levels of a quantum-mechanical, one-dimensional, anharmonic oscillator maybe approximated as 2 =(n * (n + )' En hw ;n = 0,1,2,... (++) = The parameter x, usually « 1, represents the degree of anharmonicity. Show that, to the first order in x and the fourth order in u (= ħw/kgT), the specific heat of a system of N such oscillators is given by C = Nk [(1-u² + *)+ 4x (: + *)]. 240 80 Note that the correction term here increases with temperature.
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![2) The energy levels of a quantum-mechanical, one-dimensional, anharmonic oscillator maybe
approximated as
2
=(n
* (n + )'
En
hw ;n = 0,1,2,...
(++) =
The parameter x, usually « 1, represents the degree of anharmonicity. Show that, to the first
order in x and the fourth order in u (= ħw/kgT), the specific heat of a system of N such
oscillators is given by
C = Nk [(1-u² + *)+ 4x (: + *)].
240
80
Note that the correction term here increases with temperature.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81819afa-3a34-4b66-973e-3f4b60047776%2F7eb2c775-e98e-445a-a928-5c425316c0e0%2F3ovee74.png&w=3840&q=75)
Transcribed Image Text:2) The energy levels of a quantum-mechanical, one-dimensional, anharmonic oscillator maybe
approximated as
2
=(n
* (n + )'
En
hw ;n = 0,1,2,...
(++) =
The parameter x, usually « 1, represents the degree of anharmonicity. Show that, to the first
order in x and the fourth order in u (= ħw/kgT), the specific heat of a system of N such
oscillators is given by
C = Nk [(1-u² + *)+ 4x (: + *)].
240
80
Note that the correction term here increases with temperature.
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