energy levels En of the anharmonic oscillator in the first order in the pa- rameter 3 are given by: En = hw + B(n|a*|n). Calculate the energy of the ground state Eo of the anharmonic oscillator.
energy levels En of the anharmonic oscillator in the first order in the pa- rameter 3 are given by: En = hw + B(n|a*|n). Calculate the energy of the ground state Eo of the anharmonic oscillator.
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![**Problem 2.** The potential energy of a weakly anharmonic oscillator can be modeled by:
\[ U(x) = \frac{m}{2} \omega^2 x^2 + \beta x^4, \]
where the last quartic term describes a small anharmonic correction. The energy levels \( E_n \) of the anharmonic oscillator in the first order in the parameter \( \beta \) are given by:
\[ E_n = \hbar \omega \left(n + \frac{1}{2}\right) + \beta \langle n|x^4|n \rangle. \]
Calculate the energy of the ground state \( E_0 \) of the anharmonic oscillator.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F85e4b871-9d1c-4ae2-b799-fb57954f3d49%2F3cd25dab-1501-4273-9a0f-0594ce9d85d2%2Ff66nvs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 2.** The potential energy of a weakly anharmonic oscillator can be modeled by:
\[ U(x) = \frac{m}{2} \omega^2 x^2 + \beta x^4, \]
where the last quartic term describes a small anharmonic correction. The energy levels \( E_n \) of the anharmonic oscillator in the first order in the parameter \( \beta \) are given by:
\[ E_n = \hbar \omega \left(n + \frac{1}{2}\right) + \beta \langle n|x^4|n \rangle. \]
Calculate the energy of the ground state \( E_0 \) of the anharmonic oscillator.
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