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Hamiltonian operator for particular system has energy eigenvalues En (n = 1,2,3) and corresponding normalized eigenfunctions Un. the eigenfuntions corresponding to different eigenvalues are orthogonal. The wavefuntion of the electron is given by.

Si = K(3U1 +4U2)

(a)calc real normalisation const, k

(b)what is probablity P1 that measurement of energy would give E1?

(c)...................................................................................E2?

(d)...................................................................................E3?

(e)Using p1 and P2 determine the average value for energy of the electron.

(f)Evaluate expectation vaule of hamiltionian operator for an electron in state Si and show that this is the answer obtained in (e)

numerical answers:

a) 1/5

b)9/25

c)16/25

d)0

e) (9E1+16E2)/25

I'm supposed to use what in our lectures were postlates 4 and 6.

4. something about si (x,t) = SUM (j) cj SIj (x) exp(-iEjt/hbar)

where Ej is energy associated with SIj

mmm cant write rest as with limited keyboard.

and postulate 6.

Pl = |al|^2/ SUM |an|^2 where SI = SUM (n) an SIn

Sorry I realise the type is confusing will clarify anything needed, thanks for help