- #1

zachzach

- 258

- 1

[tex]

aE_1 \psi_1+ b E_2 \psi_2 = E(\psi_1 + \psi_2)

[/tex]

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- Thread starter zachzach
- Start date

- #1

zachzach

- 258

- 1

[tex]

aE_1 \psi_1+ b E_2 \psi_2 = E(\psi_1 + \psi_2)

[/tex]

- #2

RedX

- 970

- 3

But what you're really looking for is:

[tex]

aE_1 \psi_1+ b E_2 \psi_2 = E(a\psi_1 + b\psi_2)

[/tex]

which can only be satisfied if E_1=E_2=E

- #3

zachzach

- 258

- 1

- #4

RedX

- 970

- 3

The idea is that the set of nondegenerate eigenfunctions is linearly independent. One eigenfunction cannot be the sum of two others, or else the set would not be linearly independent.

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