Aone-dimensional particle of mass m is confined within the region
0 ≤ x ≤ a and wave function ψ(x, t) = sin( πx a )e −iωt .
a by substituting the wave function ψ(x, t) into the time-dependent schr¨odinger equation show that v is independent of t.
b calculate the probability of finding the particle in the interval a 4 ≤ x ≤ 3a 4 .

Independent variable is something that is changed in a experiment. 

Sorry i don’t know what to do

Answerthe energy required is 1.60 × 10⁻¹⁸ j, to three significant figures.explanationwe define electric potential as the ratio electric potential energy to the charge,    then the following gives us the potential difference,      the formula  may be on your formula sheet.the change in electric potential energy would be the energy that would needed to move it from point a to point b. solving for that, we get    using q = 8.00  × 10⁻¹⁹ c and  δv = 2.00 v, we get    the energy required is 1.60 × 10⁻¹⁸ j, to three significant figures.

Answermuch larger;