Sign up ×  The particle in an infinite potential well in QM is
usually solved by easily solving Schrodinger differential
equation. On the other hand particle in the harmonic oscillator
oscillator potential can be solved elegantly algebraically using
the creation and annihilation operators to find its spectrum.
Is it possible to do the particle in a box problem using
creation and annihilation operator and how?  share|cite|improve
this question  1 Answer 1  up vote 3 down vote accepted  See,
e.g., the following article: "The hidden symmetry for a quantum
system with an infinitely deep square-well potential", Shi-Hai
Dong, Zhong-Qi Ma, p.520, Am. J. Phys. v.70, No.5, May 2002.
EDIT: For the infinitely deep square well, the authors establish
the creation and annihilation operators and obtain the matrix
elements of the physical quantities from the ladder operators.
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