Complexity of Solving Multi-Potential Schrodinger Equation?

In summary, the conversation discusses solving the Schrodinger equation for a potential with three regions, and also mentions finding the possible energy eigenvalues. The person asking for help is struggling with incorporating multiple potentials and is seeking assistance. The suggested approach is to match the wavefunctions at the boundaries.
  • #1
degerativpart
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Homework Statement


Does anyone now how to solve the schrodinger equation for a potenital such that: V1(0<x<a), v2(a<x<b), v3(b<x<c). Also i need to write down the condition which gives the possible energy eigenvalues of a particle in the potential. ITs easily to solve the first potential well but when it starts to introducing the two others I feel like I am messing up. Any help would be nice?


Homework Equations





The Attempt at a Solution


 
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  • #2
You basically do what you would do in a square well, except that you match the wavefunctions at the boundaries. (I'm assuming that v1, v2 and v3 are constants.)
 

Related to Complexity of Solving Multi-Potential Schrodinger Equation?

1. What is a potential well more complex?

A potential well more complex is a type of energy potential that exists in a physical system, where particles or objects are attracted towards the center of the well due to the presence of a force field. This potential is more complex because it may have multiple wells or barriers, making it more difficult to analyze and understand compared to a simple potential well.

2. How is a potential well more complex different from a simple potential well?

A potential well more complex differs from a simple potential well in that it may have multiple wells or barriers, which can lead to more complicated energy states and behaviors of particles within the system. This complexity can be caused by the presence of multiple forces or varying strengths of the force field.

3. What are some real-life examples of potential well more complex?

There are several real-life examples of potential well more complex, such as the potential energy of molecules in a chemical reaction, the gravitational potential energy of celestial bodies in a binary star system, and the electric potential energy of charged particles in a plasma.

4. How are potential well more complex analyzed and studied?

Potential well more complex are typically analyzed and studied using mathematical models and simulations, such as the Schrödinger equation in quantum mechanics or the Navier-Stokes equations in fluid mechanics. These models allow scientists to understand the behavior of particles within the system and make predictions about their energy states and movements.

5. What are the practical applications of understanding potential well more complex?

Understanding potential well more complex has practical applications in various fields, such as material science, chemical reactions, and astrophysics. It can help scientists design and develop new materials with desired properties, predict and control chemical reactions, and model the behavior of celestial bodies in space.

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