Consider a model system of five non interacting fermions in a single 3-dimensional harmonic oscillator. The Hamiltonian of a single particle is H=1/2 m \ (px2 )+ (py2 )+ (pz2 ) \+1/2 (x2+y2+z2 ) where m is the mass of the particle, on is the angular frequency, Px, Py and Pz are the momentum operators. The ground state energy of the system of non-interacting fermions is

ABC26PH0172 · Quantum Chemistry

Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Harmonic Oscillator · Exam: CSIR-NET 2018 · Marks: 2 · Difficulty: Medium

Consider a model system of five non interacting fermions in a single 3-dimensional harmonic oscillator. The Hamiltonian of a single particle is

\[ \hat{H}=\frac{1}{2 m}\left\{\left(\widehat{p_{x}^{2}}\right)+\left(\widehat{p_{y}^{2}}\right)+\left(\widehat{p_{z}^{2}}\right)\right\}+\frac{1}{2}\left(x^{2}+y^{2}+z^{2}\right) \]

where $m$ is the mass of the particle, on is the angular frequency, $\widehat{P_{x}}, \widehat{P_{y}}$ and $\widehat{P_{z}}$ are the momentum operators. The ground state energy of the system of non-interacting fermions is

(a)$\frac{21}{2} \mathrm{h} \omega$

(b)$\frac{15}{2} \mathrm{h} \omega$

(c)$\frac{5}{2} \mathrm{h} \omega$

(d)$\frac{25}{2} \mathrm{h} \omega$

Answer

Answer (as printed): A

Explanation

No explanation was printed for this question.

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