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FRI: Friday Contributed Sessions

FRI 10: Foundational / Mathematical Aspects – Unconventional Approaches

FRI 10.6: Talk

Friday, September 12, 2025, 12:00–12:15, ZHG103

Pinning quantum particles to surfaces and curves: a momentum operator- based approach — •Mohammad Shikakhwa — Department of Basic Sciences, TED University, Ziya Gökalp Caddesi No.48, 06420, Kolej - Çankaya, Ankara, Turkey

A physical, intuitive approach is proposed to confine a spin zero particle in 3D to arbitrary surfaces and curves embedded in the 3D space through the introduction of strong confining potential(s). The idea is to start from the onset with the Hamiltonian expressed in terms of the Hermitian *components* of the momentum operator and achieve confinement to the lower dimensional manifolds by dropping these Hermitian components that are normal to these manifolds along with setting the corresponding normal coordinates to zero. The resulting Hamiltonian, expressed now in terms of the manifold momenta along with a geometrical potential is a Hermitian operator. The resulting manifold momenta are at the kinematical ones proportional to the velocity of the particle on these manifolds.

Keywords: geometrical momentum; Hamiltonian on a surface; Hamiltonian on a curve; constraints; thin layer quantization