In the input section of the script qp_rules.m you specify: The initial and final states. The saving of an animated gif of the probability cloud. The display of the animation of the probability cloud. Can select a contour plot or a surf plot. The maximum radial distance for the radial wavefunction r_max. This is an important variable for accurate predicts of the lifetime of the excited state. The value of r_max cannot be too small or too large when implementing the numerical procedure to solve the radial wave equation. Figure 1 shows the plot of the radial function functions for the initial and final states for one simulation with r_max = 30x10-9 m. The plots show that the wavefunctions approaches zero in an appropriate fashion. The calculated lifetime is 1168 ns. Figure 2 shows the wavefunction plots for r_max=10x10-9 m. The tail is not a good representation of the wavefunction and the calculated of the lifetime is 246 ns and is not an accurate result. Fig. 1. Accurate plots of the wavefunctions when r_max = 30x10-9 m. Fig. 2. Incorrect plots of the wavefunctions when r_max = 10x10-9 m. Excited states and transition rates in a hydrogen atom If a hydrogen atom is excited to a higher energy level, it will at some later time spontaneously make transitions to successively lower energy levels. In a transition from a higher energy state (1) to a lower energy state (2), the frequency and wavelength of the emitted photon is
In the input section of the script qp_rules.m you specify: The initial and final states. The saving of an animated gif of the probability cloud. The display of the animation of the probability cloud. Can select a contour plot or a surf plot. The maximum radial distance for the radial wavefunction r_max. This is an important variable for accurate predicts of the lifetime of the excited state. The value of r_max cannot be too small or too large when implementing the numerical procedure to solve the radial wave equation. Figure 1 shows the plot of the radial function functions for the initial and final states for one simulation with r_max = 30x10-9 m. The plots show that the wavefunctions approaches zero in an appropriate fashion. The calculated lifetime is 1168 ns. Figure 2 shows the wavefunction plots for r_max=10x10-9 m. The tail is not a good representation of the wavefunction and the calculated of the lifetime is 246 ns and is not an accurate result. Fig. 1. Accurate plots of the wavefunctions when r_max = 30x10-9 m. Fig. 2. Incorrect plots of the wavefunctions when r_max = 10x10-9 m. Excited states and transition rates in a hydrogen atom If a hydrogen atom is excited to a higher energy level, it will at some later time spontaneously make transitions to successively lower energy levels. In a transition from a higher energy state (1) to a lower energy state (2), the frequency and wavelength of the emitted photon is
qp_rules.docx