Raising and lowering operator coefficients

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SUMMARY

The discussion focuses on the manipulation of raising and lowering operators in quantum mechanics, specifically the coefficients of the expression ad^(2) + a*ad + ad*a + a^(2). The operators are defined as ad|n>=sqrt(n+1)|n+1> and a|n>=sqrt(n)|n-1>. The user initially struggles with the problem but ultimately resolves it, indicating a common challenge in understanding operator algebra.

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  • Understanding of quantum mechanics and operator algebra
  • Familiarity with raising and lowering operators
  • Knowledge of the notation used in quantum states, such as |n>
  • Basic grasp of mathematical manipulation of operators
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davidj89
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Homework Statement


where a=lowering operator, ad=raising operator
ad^(2)+a*ad+ad*a+a^(2)
just need to find the coefficients

Homework Equations


ad|n>=sqrt(n+1)|n+1>
a|n>=sqrt(n)|n-1>

The Attempt at a Solution


ad^(2)=?|n+2>
ad*a=n|n>
a*ad=n|n>
a^(2)=?|n-2>
just reviewing and can't get this practice problem, I think this is where I am messing up.
 
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never mind I got it, how do I delete my post?
 

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