Given (1/2) |ej> + (v3/2) |e2> , |ej> and |e2> are solutions of a hamiltonian, h, which is not the hamiltonian of a harmonic oscillator, (a) what is the physical meaning of the expression: h |e,> = e1 |ej> ? 4. (5) (6) (b) what are the conditions imposed on ej> and |e2> for the expansion of v> to be physically meaningful? (je2> satisfies the equation in (a) too.) (c) express jy> in the- representation and explain the meaning of (8) x (1/2) in . is the expansion of ly> consistent with the concept of the hilbert space? explain your answer. (d) what is the physical meaning of < h? should it be divided by give the reason of your answer

ι вєℓιєνє ιт ιѕ тнє fιяѕт ¢нσι¢є(α.)

нє ѕнσυℓ∂ ѕмιℓє ρσℓιтℓу αи∂ ѕρєαк тσ тнє ρєяѕσи ωнσ ιѕ ιитєяяυριиg αfтєя тнє ∂ιѕ¢υѕѕισи

нσρє ι ¢συℓ∂ нєℓρ.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .