A particle of mass m is confined in the potential \[V ( x ) = \ array*20c 1/2m ^2x^2,& for x < 0 \\ ,& for x 0 array .\] Let the wave function of the particle be given by ( x ) = - 1 5 _0 + 2 5 _1 where _0 and _1 are the eigen functions of the ground state and the first excited slate respectively. The expectation value of the energy is

A particle of mass m is confined in the potential

V\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{2}m{\omega ^2}{x^2},}&{{\text{for }}x < 0} \\ {\infty ,}&{{\text{for }}x \leqslant 0} \end{array}} \right.
Let the wave function of the particle be given by $$\psi \left(x\right)=-\frac{1}{\sqrt{5}}{\psi }_0+\frac{2}{\sqrt{5}}{\psi }_1$$
where $${\psi }_0$$ and $${\psi }_1$$ are the eigen functions of the ground state and the first excited slate respectively. The expectation value of the energy is

Answer: Option C