Question

10,000 measurements are made of the energies of a particle in a box with infinite potential walla a distance L, apart. The results of the measurements are

E1 occurs 2000 times

E2 Occurs 5000 times

E3 occurs 3000 times

obtain the probabilitites of each of the measured energies and from this the coefficient of an expression of the tie dependent wave function

Answer 1

P(E1) = 2000/10000 = 2/5

P(E2) = 5000/10000 = 1/2

and P(E3) = 3000/10000 = 3/10

P(E1)+P(E2)+P(E3) = 1;

let

thus

thus

and

and

note that sum satisfies the completeness condition

thus wavefunction is

and time dependent wavefunction

if you wish to substitute the equations for

and for values of n = 1,2,3 you can.