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In a one-dimensional harmonic oscillator, are respectively the ground, first and the second existed states. These three states are normalized and are orthogonal to one another. 
ψ1 and ψ2 are two states defined by

where a is a constant.
The value of a for which y2 is orthogonal to y1 is ___________ .
Correct answer is '-1'. Can you explain this answer?
Verified Answer
In a one-dimensional harmonic oscillator, are respectively the ground,...

for orthogonal condition -

1 + 2 + 3a = 0 
3a = - 3
a = -1
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In a one-dimensional harmonic oscillator, are respectively the ground, first and the second existed states. These three states are normalized and are orthogonal to one another.ψ1 and ψ2 are two states defined bywhere a is a constant.The value of a for which y2 is orthogonal to y1 is ___________ .Correct answer is '-1'. Can you explain this answer?
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