Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Postulates Operators · Exam: NET JUNE 2014 · Marks: 2 · Difficulty: Medium
A particle in a one-dimensional box (potential zero between to a and infinite outside) has the ground state energy $E_{0}=\frac{0.125 h^{2}}{m a^{2}}$. The expectation value of the above Hamiltonian with yields an energy $E_{1}$. Using a linear combination of two even functions $\mathrm{x}(\mathrm{x}-\mathrm{a})$ and $\mathrm{x}^{2}(\mathrm{x}-\mathrm{a})^{2}$ we obtain variational maximum to the ground state energy as E 2 . Which of the following relations holds for $\mathrm{E}_{0}, \mathrm{E}_{1}$ and $\mathrm{E}_{2}$ ?
(a)$\mathrm{E}_{0}<\mathrm{E}_{1}<\mathrm{E}_{2}$
(b)$\mathrm{E}_{0}<\mathrm{E}_{2}<\mathrm{E}_{1}$
(c)$\mathrm{E}_{1}<\mathrm{E}_{0}<\mathrm{E}_{2}$
(d)$\mathrm{E}_{2}<\mathrm{E}_{0}<\mathrm{E}_{1}$
Answer
SELF-PRACTICE — the source book printed no answer.
Nothing is invented here, so this question has no answer on record.