Continuity of the wave function

[pi11]

actually i have my exam and i am really weak in quantum mechanics ... i would like to know another question sir ... i know the physical meaning of normalization , will you please tell me the physical meaning of orthogonality ? i have one more small assignment too .. i tried but unable to do ... the question is that if H is an operator of an eigen function U1 with eigen value E1 and H is an operator of an eigen function U2 with eigen value E2 then show that H is also an operator of the eigen function U1+U2.

 

[bhobba]

actually i have my exam and i am really weak in quantum mechanics ... i would like to know another question sir ... i know the physical meaning of normalization , will you please tell me the physical meaning of orthogonality ? i have one more small assignment too .. i tried but unable to do ... the question is that if H is an operator of an eigen function U1 with eigen value E1 and H is an operator of an eigen function U2 with eigen value E2 then show that H is also an operator of the eigen function U1+U2.

This really belongs in the homework help section.

But I will answer the orthogonality question by asking you to apply the Born rule to orthogonal states.

Since they are eigenfunctions H*U1 = E1*U1 and H*U1 = E1*U1 so H*(U1 +U2) = H*(E1 + E2) so E1 + E2 is an eigenvalue of H with eigenfunction U1+U2.

Thanks
Bill