WKB Approximation: Suggestions for Starting Points

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Thread starter Mrinmoy Naskar
Start date Mar 28, 2016
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Approximation Wkb Wkb approximation

In summary, the WKB approximation method is a mathematical technique used to approximate the solution of a differential equation with a rapidly varying amplitude. It is commonly used in quantum mechanics, optics, and fluid mechanics to solve equations for systems with varying potential energies. The method involves finding turning points and determining a semiclassical parameter to divide the system into regions where the approximation is valid. However, the method has limitations for systems with large variations in potential energy or multiple turning points, and does not account for quantum effects. Alternative methods, such as the variational and perturbation methods, exist but the WKB approximation method remains widely used due to its simplicity and effectiveness in certain systems.

Mar 28, 2016

Mrinmoy Naskar

Any good book for starting wkb approximation except Griffth... Please suggest some...

Last edited by a moderator: Mar 28, 2016

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Mar 28, 2016

ddd123

Liboff explained every detail but not very advanced. Shankar was more advanced.

Related to WKB Approximation: Suggestions for Starting Points

1. What is the WKB approximation method?

The WKB approximation method is a mathematical technique used to approximate the solution of a differential equation with a rapidly varying amplitude. It stands for Wentzel-Kramers-Brillouin and is also known as the semiclassical or eikonal approximation.

2. When is the WKB approximation method used?

The WKB approximation method is commonly used in quantum mechanics to solve the Schrödinger equation for systems with varying potential energies. It is also used in other areas of physics, such as optics and fluid mechanics.

3. What are the starting points for using the WKB approximation method?

The starting points for using the WKB approximation method are finding the turning points and determining the semiclassical parameter, which is a measure of the rapidity of the amplitude variation in the system. These points are used to divide the system into regions where the WKB approximation is valid.

4. What are some limitations of the WKB approximation method?

The WKB approximation method is not suitable for systems with large variations in potential energy or for systems with multiple turning points. It also does not account for quantum effects, such as tunneling, and is only accurate for systems with high energy levels.

5. Are there any alternatives to the WKB approximation method?

Yes, there are alternative methods for solving differential equations with varying amplitude, such as the variational method and the perturbation method. However, the WKB approximation method is still widely used due to its simplicity and effectiveness in certain systems.