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snkk197
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I've been combing over websites and papers on this, but I can't get a handle on trying to explain or visualize the similarity between them. The wave equation "smears out" over time as does the diffusion equation?
Schrodinger's equation is a fundamental equation in quantum mechanics that describes the time evolution of a quantum system. It is used to calculate the probability of finding a particle in a certain location at a certain time.
The Diffusion equation is a partial differential equation that describes how a substance (such as heat or particles) diffuses through a medium over time. It is used in a wide range of fields, including physics, chemistry, and biology.
While both equations involve the concept of probability and time evolution, Schrodinger's equation is used to describe the behavior of quantum particles, while the Diffusion equation is used to describe the behavior of substances in a macroscopic scale.
Schrodinger's equation is used in a variety of fields, including quantum mechanics, nuclear physics, and solid state physics. The Diffusion equation has applications in fields such as thermodynamics, fluid mechanics, and chemical reactions.
Both equations have limitations in their applicability. Schrodinger's equation does not take into account relativistic effects, and the Diffusion equation is only valid for substances that follow Fick's laws of diffusion. Additionally, both equations may not accurately describe systems with a large number of particles or complex interactions.