Non-Adiabatic Crossing of Energy Levels.

Non-Adiabatic Crossing of Energy Levels.

July 19, 1932 | By CLARENCE ZENER, National Research Fellow of U.S.A.
The paper by Clarence Zener discusses the non-adiabatic crossing of energy levels in molecules, focusing on the transition between polar and homopolar states. The key points are: 1. **Introduction**: - The adiabatic theorem states that if a parameter changes slowly, the system remains in the same state. - If the parameter changes with a finite velocity, the system can transition between states. - The transition probability is calculated using linear combinations of the eigenfunctions. 2. **Analysis**: - The problem is simplified by assuming that the relative kinetic energy of the two systems is much smaller than the energy difference. - The transition region is assumed to be small, allowing the energy difference to be treated as a linear function of time. - The wave equation is transformed into a system of first-order differential equations. - The solutions are expressed in terms of the Weber function, and the transition probability is derived. 3. **Discussion**: - The transition probability is influenced by the relative velocity and the nature of the energy difference. - Two cases are considered: one where the energy difference is constant and the other where it is a linear function. - The transition probability is shown to depend on the relative velocity in a similar manner. - The effective cross section for collisions is calculated, considering the transitional region around the internuclear distance. In conclusion, the paper rigorously calculates the transition probability when a parameter is varied with a finite velocity, providing insights into the non-adiabatic behavior of molecular systems.The paper by Clarence Zener discusses the non-adiabatic crossing of energy levels in molecules, focusing on the transition between polar and homopolar states. The key points are: 1. **Introduction**: - The adiabatic theorem states that if a parameter changes slowly, the system remains in the same state. - If the parameter changes with a finite velocity, the system can transition between states. - The transition probability is calculated using linear combinations of the eigenfunctions. 2. **Analysis**: - The problem is simplified by assuming that the relative kinetic energy of the two systems is much smaller than the energy difference. - The transition region is assumed to be small, allowing the energy difference to be treated as a linear function of time. - The wave equation is transformed into a system of first-order differential equations. - The solutions are expressed in terms of the Weber function, and the transition probability is derived. 3. **Discussion**: - The transition probability is influenced by the relative velocity and the nature of the energy difference. - Two cases are considered: one where the energy difference is constant and the other where it is a linear function. - The transition probability is shown to depend on the relative velocity in a similar manner. - The effective cross section for collisions is calculated, considering the transitional region around the internuclear distance. In conclusion, the paper rigorously calculates the transition probability when a parameter is varied with a finite velocity, providing insights into the non-adiabatic behavior of molecular systems.
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