Any help appreciated.

a particle in a 1-dimensional box, and variational method is required.

trial wavefunction is Φ(x) =Ax(L-x)+B(x^2)*(L-x)^2

L is the length and = 52.9pm (bohr radius);

m=me =9.11*10^(-31) kg

when I plug in numbers into equations

E_= α_{B} + β^2/(α_{B}-α_{A})

E_{+}= α_{A} - β^2/(α_{B}-α_{A})

I got numbers like 1.07*10^(-111) for E_ and 2.99*10^(-70) for E_{+}, and compare to E= n^2*Pi^2/2 they are way off. I just cant figure out where I did wrong. Units do not make any sense when I try to solve α_{B} and α_{A} and β:

α_{B} = h(reduced) ^2* L^7/105m

α_{A} = h(reduced) ^2* L^3/6m

β = h(reduced) ^2* L^5/30m

Shouldn't they all be in the unit of energy?

but these are not ...

and after obtaining wavefunction and probablity, why are probablities different here while they are equal for a regular particle-in-a-box?