Python Wave Function

This lab was a much different lab in all the rest because it required the use of computer programming using the language of phython. The ultimate goal or objective of this experiment is simply stated in the title. This allows students to be easier to visualize and see what is really going on to the uncertainty principle and how it relates to their construction. The programs that were used in this laboratory experiment was python, vpyton and pylab were to be installed prior to starting the lab.

Particles that are in a definite energy state like an electron bound which is not in an infinite energy level in an atom. The value of the absolute value of psi squared is independent of time, which is called a stationary state. If the definite energy E and the time dependent wave function can be written as a product of the time independent function and a function of time. The Schrodinger equation for a particle with definite energy E is:

Treating the wave function as a separable differential function, it can be seperated into a part that depends on x and one that depends on time. Taking the partial derivative with respect to time and the space portion constant comes out in front, this can be plugged back into the schrodinger equation and then divide both sides by psi of x times f of time. Rearrangement and cleaning up allows

The plot of a Gaussian distribution is one of the tasks for this assignment. In the informal form of psuedocode, the mean average and the standard deviation is set as constant, which is the followed by the coefficient of one over sigma root 2 pi. An initialized list called Gauss was then created and the function for gauss was coeff*e^-(x-avg)^2/2sigma^2. The final step was to write plot(x,Gauss). A graph that had a bell curve was then shown. This really shows that the probability that the particle is in a certain region gets much larger at a certain point and gets less and less at all other parts.

Another step or objective from this lab was to plot a sinusoidal function instead of a bell curve. This is surprisingly not that much more difficult, however it does require that some adjustments are made not only to the equation being used, but also to the boundaries of the sinusoid. The bounds used in this particular lab were set between the values of positive and negative pi. The program was also designed so that the amplitude and period of the sine function can be varied. This is accomplished by defining the variable of the amplitude. The frequency coefficient was also defined with a loop so that it could repeat itself to get a better view of whats going on.

The experiment was a different approach at tackling labs and understanding concepts because the probability of finding the particle and actually finding the particle cannot be determined using lab equipment found in community colleges. This laboratory may have been frustrating for some at first but once one gets the hang of it, it is not really that bad. Graphs of any type can be accomplished plotted and varied from any view. There is really no uncertainty in this lab which is one of the few labs like that. The only uncertainty is being uncertain that the program will work correctly.