Run Cheng

We establish a quantum dynamics framework for curved submanifolds embedded in higher-dimensional spaces. Through rigorous dimensional reduction, we derive the first complete Schr\"{o}dinger and Klein-Gordon equations incorporating…

In Foldy-Wouthuysen representation, we deduce the effective quantum mechanics for a particle confined to a curved surface by using the thin-layer quantization scheme. We find that the spin effect caused by confined potential as the results…

We investigate the statistical distribution for ideal Bose gases with constant particle density in the 3D box of volume $V=L^{3}$. By changing linear size $L$ and imposing different boundary conditions on the system, we present a numerical…

Noninteracting electrons confined to a corrugated surface are investigated in magnetic field, and the associated effective Pauli equation is given analytically by the thin-layer quantization scheme. Interestingly, the Zeeman splitting gaps…

In the spirit of the thin-layer quantization scheme, we give the effective Hamiltonian describing the noninteracting electrons confined to an annular corrugated surface, and find that the geometrically induced potential is considerably…

In the spirit of the thin-layer quantization scheme, we give the effective Shr\"{o}dinger equation for a particle confined to a corrugated torus, in which the geometric potential is substantially changed by corrugation. We find the…