The wave function of a particle in a one-dimensional potential at time t = 0 is $$\psi \left( {x,\,t = 0} \right) = \frac{1}{{\sqrt {15} }}\left[ {2{\psi _0}\left( x \right) - {\psi _1}\left( x \right)} \right]$$       where, $${\psi _0}\left( x \right)$$  and $${\psi _1}\left( x \right)$$  are the ground arid the first excited states of the particle with corresponding energies E₀ and E₁. The wave function of the particle at a time t is

A. $$\frac{1}{{\sqrt 5 }}{e^{ - i\left( {{E_0}{E_1}} \right)t/2h}}\left[ {2{\psi _0}\left( x \right) - {\psi _1}\left( x \right)} \right]$$

B. $$\frac{1}{{\sqrt 5 }}{e^{ - i{E_0}t/h}}\left[ {2{\psi _0}\left( x \right) - {\psi _1}\left( x \right)} \right]$$

C. $$\frac{1}{{\sqrt 5 }}{e^{ - i{E_1}t/h}}\left[ {2{\psi _0}\left( x \right) - {\psi _1}\left( x \right)} \right]$$

D. $$\frac{1}{{\sqrt {15} }}\left[ {2{\psi _0}\left( x \right){e^{ - i{E_0}t/h}} - {\psi _1}\left( x \right){e^{ - i{E_1}t/h}}} \right]$$

Answer: Option D