- #1
Plutoniummatt
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Homework Statement
[tex]\phi_1[/tex] and [tex]\phi_2[/tex] are normalized eigenfunctions of observable A which are degenerate, and hence not necessarily orthogonal, if <[tex]\phi_1[/tex] | [tex]\phi_2[/tex]> = c and c is real, find linear combos of [tex]\phi_1[/tex] and [tex]\phi_2[/tex] which are normalized and orthogonal to: a) [tex]\phi_1[/tex]; b) [tex]\phi_1[/tex]+[tex]\phi_2[/tex]
Homework Equations
Non?
The Attempt at a Solution
attempt at a)
from the fact that <[tex]\phi_1[/tex] | a[tex]\phi_1[/tex] + b[tex]\phi_2[/tex]> = 0
i got a + bc = 0
if I let b = 1, then a = -c,
then if i use the fact that it must be normalised:
<a[tex]\phi_1[/tex] + b[tex]\phi_2[/tex] | a[tex]\phi_1[/tex] + b[tex]\phi_2[/tex]> = 1,
both equations can't be satisfied simultaneously? Where am i going wrong? thanks