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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.

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.
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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