Linear algebra, eigenvalues, linear combinations, complex numbers.

[lavenderblue]

Help with Quantum please!

If a1=a2=a then show that any linear combination
(psi)=a1(psi)1 + a2(psi)2, where a1 and a2 re arbitrary complex numbers, is also an eigenstate with th same eigenvalue i.e. show that A(psi)=a(psi)

Could you please show your full workings I don't know where to start :(. Thanks!

Here's what I thought might be right, but I'm not quite sure...

where A(psi)1=a(psi)1 and A(psi)2=a(psi)2
<A> = the integral (psi)*(A)(psi)

 

[G01]

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