How do I solve the Schrodinger wave equation with a differential equation?

In summary, the Schrodinger wave equation is a fundamental equation in quantum mechanics that describes the behavior of particles in terms of their wave-like properties. It was developed by Austrian physicist Erwin Schrodinger in 1926 and is significant because it provides a mathematical framework for understanding the behavior of particles at the atomic and subatomic level. It differs from classical mechanics in that it describes the behavior of particles in terms of probability rather than definite outcomes. However, it can only be solved exactly for a few simple systems and in most cases, approximate solutions must be found using numerical methods.
  • #1
vmercel
1
0
in solving the schrodinger wave equation, there arises this differential equation

(d^2/dx^2) ψ + (1/x) (d/dx )ψ + (a/x)ψ + (b/x^2)ψ + cψ = 0

Please any leads on how to solve this equation will be highly appreciated.
 
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  • #2
Suggest you ask this over in the Diff Eq forum
 

1. What is the Schrodinger wave equation?

The Schrodinger wave equation is a fundamental equation in quantum mechanics that describes the behavior of particles in terms of their wave-like properties. It is used to determine the probability of finding a particle at a certain location in space and time.

2. Who developed the Schrodinger wave equation?

The Schrodinger wave equation was developed by Austrian physicist Erwin Schrodinger in 1926. He was awarded the Nobel Prize in Physics in 1933 for his contributions to the field of quantum mechanics.

3. What is the significance of the Schrodinger wave equation?

The Schrodinger wave equation is significant because it provides a mathematical framework for understanding the behavior of particles at the atomic and subatomic level. It allows scientists to make predictions about the behavior of particles and has been crucial in the development of modern technology, such as transistors and lasers.

4. How is the Schrodinger wave equation different from classical mechanics?

The Schrodinger wave equation is different from classical mechanics in that it describes the behavior of particles in terms of probability rather than definite outcomes. In classical mechanics, the behavior of particles is determined by their exact position and velocity, while in quantum mechanics, particles are described in terms of a wave function that represents the probability of finding them in a certain state.

5. Can the Schrodinger wave equation be solved exactly for all systems?

No, the Schrodinger wave equation can only be solved exactly for a few simple systems. In most cases, it is only possible to find approximate solutions using numerical methods. This is due to the complexity of the equation and the limitations of our current understanding of quantum mechanics.

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