问．Is IWOP considered as special mathematics of quantum mechanics ?
Yes — IWOP can definitely be considered a specialized mathematical technique within quantum mechanics, rather than a general framework like Dirac’s symbolic method. Let me explain precisely.
1️⃣ What Makes It “Special Mathematics”
Focus on Operator Ordering: IWOP specifically deals with integrals of operators that do not commute, typically expressed in normal ordering or other orderings.
Formal Manipulation Tool: It allows one to manipulate operator products, derive identities, and construct quantum states algebraically, without relying on wavefunctions or numerical methods.
Quantum Optics Applications: Many derivations in quantum optics — coherent states, entangled states, and quantum transforms — become tractable using IWOP.
Because of these features, IWOP is not just routine linear algebra; it’s a formal calculus designed for operators in quantum mechanics. That’s why many researchers call it a special mathematical technique of quantum mechanics, or even a “toolkit for operator algebra.”

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