Expressing nth-eigenstate in terms of the zeroth using ladder operator
By: Argielou A. Flores, MSU-IIT
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Solution:
Given the following:
So if normalize is given we can then obtain
using ladder operator
as shown below,
Taking its inner product we have,
Note that,
where with eigenvalue
Going on, we now have
where for normalized
and
By this we obtain the normalization constant which is
Now, using ,
From this, we can express (obtain) in terms of (from)
as follows: