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Freddy Cisneros
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I am trying to plot the wave-function of free particles as a function of x and time. Can someone explain or reference a site which explains how.
--Thank you
--Thank you
RaulTheUCSCSlug said:So for this, it will be helpful if you understand a bit of multivariable calculus. Since the plot will not only be a function of time, but also a function of space (x,t) so your function now has two variables. We know this for a fact, because we encounter it in our daily lives. (at least we perceive it to be such a fact) Now looking at standard equation of a wave :
We see how a function might change as x, and t changes. But much of the time, one parameter may seem rather arbitrary, and that parameter may be time.
I know that I am getting a bit off topic, but use the standard equations of a wave to guide you on what you want to plot. I believe Wolfram alpha has the ability to plot functions of several parameters if I am not mistaken. Experiment, and have a little fun with it. :)
Freddy Cisneros said:Raul,
Thanks, and yeah I have been trying to plot the Solution to the Schrödinger equation for a free particle using Wolfram they have an interactive option where you can play around with the wave. However when plotting
$$\Psi(x,t)=e^{ikx-wt}$$
and I have x fixed, the real and imaginary components do not oscillate vertically with time. Maybe Python will do the trick?
--Freddy Cisneros
RaulTheUCSCSlug said:Damn, yeah maybe python can do the trick, or C. But that goes beyond the realm of my knowledge.
A time-dependent wave-function is a mathematical representation of a quantum mechanical system that evolves over time. It describes the probability amplitude of finding a particle at a certain position and time.
To plot a time-dependent wave-function, you will need to use a computer program or software that can solve the Schrodinger equation. This equation is a fundamental equation in quantum mechanics that describes the evolution of a wave-function over time. By inputting the necessary parameters and initial conditions, the program will calculate the wave-function at different points in time and plot it on a graph.
Plotting time-dependent wave-functions allows us to visualize the behavior of quantum systems over time. It can help us understand the dynamics of particles and their interactions, and make predictions about their future states. It is also an essential tool in studying and developing quantum technologies.
The ability to plot time-dependent wave-functions depends on the complexity of the quantum system. Simple systems, such as a single particle in a potential well, can be easily plotted. However, for more complex systems with multiple particles and interactions, it may not be possible to plot the wave-function analytically and would require numerical methods.
One limitation of plotting time-dependent wave-functions is that it only provides a probabilistic description of a system. The wave-function represents the probability of finding a particle at a certain position and time, but it does not provide information about the particle's exact position or momentum. Additionally, the accuracy of the plotted wave-function depends on the accuracy of the initial conditions and the assumptions made in solving the Schrodinger equation.