Electronic State Transitions

For the time evolution of an energy state composed of different contributions from other states. Where these functions are eigenfunctions at time equals zero. But at a later time, these functions may have different contributions to the overall quantum state. The expansion coefficients describing the contributions of these states to the overall state will vary with time. Because the existing stationary states describe the system at the initial timepoint, these states can still be used at different times, but the overall contributions may be different at different times. If the overall system changes, the Hamiltonian describing the overall energy state will also change. The system could change due to a number of different reasons, such as shining light on the system.

Take for example the transition of an electron in a hydrogen atom moving from a 1s orbital to a 2p orbital. When the electron is in the 1s orbital, the contribution of the 1s orbital to the system is 1, while the contribution of the 2p orbital to the system is 0. The electron is found in the 1s orbital and thus the contribution to the system is only due to the 1s orbital. If a photon with the proper frequency comes in, the electron will be able to move from the 1s orbital to the 2p orbital. At a later time after the photon enters the system, the contribution of the 1s orbital will then become 0 while the contribution of the 2p orbital is 1, as the electron is now found in the 2p orbital.

The program below demonstrates this concept by applying an oscillating electric field (like light) to a system, and the effect of this oscillating electric field can be visualized by observing how other states then become populated. If the energy of the photon is sufficient enough for the transition to occur, higher energy states can also be populated.

The energy state itself appears to oscillate because the force is equal to the negative slope of the potential function. When the slope of the potential is downward, the force moves to the left, and when the slope of the potential is upward, the force moves to the right. While the potential well is defined and constant, the potential of the oscillating electric field does change with time, and this is why the graph appears to oscillate over time.