ABC26PH1244 · Quantum Chemistry

Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Particle In A Box · Exam: NET DEC 2013 · Marks: 2 · Difficulty: Medium

Consider a particle in a one dimensional box of length 'a' with the following potential
\[ \begin{array}{ll} \mathrm{V}(\mathrm{x})=\omega & \mathrm{x}<0 \mathrm{V}(\mathrm{x})=\omega & \mathrm{x}>\mathrm{a} \mathrm{V}(\mathrm{x})=0 & 0 \leq \mathrm{x} \leq \mathrm{a} / 2 \mathrm{V}(\mathrm{x})=\mathrm{V}_{1} & \mathrm{a} / 2 \leq \mathrm{x} \leq \mathrm{a} \end{array} \]
Starting with the standard particle in a box Hamiltonian as the zero ${ }^{\text {th }}$ order Hamiltonian and the potential of $\mathrm{V}_{1}$ from 'a/2' to 'a' as a perturbation, the first order energy state is
(a)$\mathrm{V}_{1}$
(b)$\mathrm{V}_{1} / 4$
(c)$-\mathrm{V}_{1}$
(d)$\mathrm{V}_{1} / 2$
Answer
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Explanation
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