Quantum mechanics in power-law potentials

V. G. de Paula, Wanisson Silva Santana, Clebson Cruz +1 more

叶卓林, 李卫胜, 赖益铭 +2 more

We propose a quantum-mechanical Brayton engine model that works between two superposed states,employing a single particle confined in an arbitrary power-law trap as the working substance. Applying the superposition principle,we obtain the explicit expressions of the power and efficiency,and find that the efficiency at maximum power is bounded from above by the function: η+= θ/(θ+1),with θ being a potential-dependent exponent.

Konstantin V. Kazakov

Zhuolin Ye, Weisheng Li, Yiming Lai +2 more

Abstract We propose a quantum-mechanical Brayton engine model that works between two superposed states, employing a single particle confined in an arbitrary power-law trap as the working substance. Applying the superposition principle, we obtain the explicit expressions of the power and efficiency, and find that the efficiency at maximum power is bounded from above by the function: η + = θ/(θ + 1), with θ being a potential-dependent exponent.

Jacob Katriel

The naïve Bohr quantization condition mvr=nℏ is applied to arbitrary spherically symmetric power-law potentials. The dependence of the energy eigenvalues on the principal quantum number n agrees with fully quantum mechanical results either exactly (for the hydrogen atom, the harmonic oscillator, and the infinite square well) or asymptotically (the linear potential). This naïve treatment can be used in precalculus, high-school, or “quantum theory for poets” expositions.