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.