Geometric Proof of Exact Quantization Rules in One Dimensional Quantum Mechanics |
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| Authors: | M X Shao Y Z Mao and D T Zhang |
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| Institution: | (1) Physics Department, Henan Polytechnic University, Jiaozuo, 454000, China;(2) School of Physical Science and Technology, Lanzhou University, Lanzhou, 730000, China |
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| Abstract: | In terms of the construction of vector field with momentum and logarithmic derivative of wavefunction as its components, a
geometric proof of an exact quantization rule in one dimensional quantum mechanics systems is given. The quantization rule
arises from the SO(2) gauge transformation. In addition, the quantization rule is generalized to the case when the potential function is piecewise
continuous between the two turning points.
This work was supported by doctoral foundation of HPU. |
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| Keywords: | Quantization rule Gauge transformation Piecewise continuous |
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