Wave function (schrodinger equation)

In summary, the conversation discusses sketching the wave function for a particle with energy E in a potential well and correctly representing the amplitude and wavelength in different regions. The solution involves graphing a rough sketch of the wave function, with oscillation occurring when E>V0 and a free particle-like solution with varying frequencies in the region where the energy is greater than the potential. However, there are two questionable parts in the solution, such as the absence of decay before the first measurable wall and the slow oscillation in the second well with only a 2 unit difference.
  • #1
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Homework Statement


Sketch the wave function ψ(x) corresponding to a particle with energy E in the potential well shown below. Show correctly relative values of amplitude and wavelength in different regions.

wavefunc.png



Homework Equations


none?


The Attempt at a Solution


I guess I was a bit confused how to get started with this.. there's nothing like this in my notes so I'm kinda guessing. but from the picture I can see E is a staight line (constant) and it only oscillates when E>V0 otherwise it is decaying (e^x or something). So i graphed rough sketch of the wave function..am I doing anything that is wrong?
 
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  • #2
Your understanding of what to do is correct. Of course in the region when the energy of the particle is greater than the potential: one measures a free particle like solution with varying frequencies.

There are two questionable parts for me in your solution. There isn't a decay before the first measurable wall and the second well oscillates too slowly being only 2 units higher than the first.
 

1. What is the Schrodinger equation?

The Schrodinger equation is a mathematical formula that describes the behavior of quantum particles, such as electrons, in a given system. It was developed by Austrian physicist Erwin Schrodinger in 1926.

2. What does the wave function represent?

The wave function represents the probability of finding a quantum particle in a particular state at a given time. It is a complex-valued function that describes the particle's position, momentum, and other properties.

3. How is the Schrodinger equation solved?

The Schrodinger equation is typically solved using mathematical techniques, such as separation of variables and Fourier transforms. Solutions to the equation provide information about the possible energy states and corresponding wave functions of a quantum system.

4. What is the significance of the Schrodinger equation in quantum mechanics?

The Schrodinger equation is one of the fundamental equations of quantum mechanics, along with the Heisenberg uncertainty principle and the Pauli exclusion principle. It allows scientists to make predictions about the behavior of quantum particles, and has been instrumental in our understanding of the micro world.

5. Can the Schrodinger equation be applied to macroscopic systems?

The Schrodinger equation is typically used to describe the behavior of microscopic particles, such as atoms and molecules. However, it has also been successfully applied to macroscopic systems, such as superconductors and superfluids. In these cases, the equation is often modified to account for collective behavior of particles.

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