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ladder operator
In linear algebra (and its application to quantum mechanics), a raising or lowering operator (collectively known as ladder operators) is an operator that increases or decreases the eigenvalue of another operator. In quantum mechanics, the raising operator is sometimes called the creation operator, and the lowering operator the annihilation operator. Well-known applications of ladder operators in quantum mechanics are in the formalisms of the quantum harmonic oscillator and angular momentum.
== History ==
Many sources credit Dirac with the invention of ladder operators.〔http://www.fisica.net/quantica/quantum_harmonic_oscillator_lecture.pdf〕 Dirac's use of the ladder operators shows that the total angular momentum quantum number needs to be a non-negative ''half'' integer multiple of ħ. The restriction on and to integer multiples of ħ was done by "H. E. Rorschach at the 1962 Southwestern Meeting of the American Physical Society." There also may have been resistance to such a split by Merzbacher. The ladder operators have been extended many times, to deal with spin, and to generate l.
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