Prove Van Leeuwen's Theorem: Diamagnetism Does Not Exist in Classical Physics

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In summary, the conversation discusses proving Van Leeuwen's theorem, which states that diamagnetism does not exist in classical physics. The participants mention the Hamiltonian and the induced magnetization, and one person shares their solution to the problem by shifting integration variables.
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Henk
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For a statistical mechanics course we have to prove Van Leeuwen's theorem: Diamagnetism does not exist in classical physics.

I know that in an external magnetic field H the Hamiltonian Ha goes from Ha(p1,p2,--------,pN ,q1,q2,-------qN) to Ha(p1-(e/c)A1, p2-(e/c)A2, ------- pN-(e/c)AN, q1,q2,------.qN)

I also know that the induced magnetization M = kT*d(log QN)/dH

So the problem is finding QN. I know how to calculate it for a perfect gas without the magnetic field but I can't seem to solve the integral when Ha changes.
 
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  • #2
Try shifting integration variables.
 
  • #3
Ah I found bij changing p - (e/c)A to p' and then integrating. Thanks a lot.
 

FAQ: Prove Van Leeuwen's Theorem: Diamagnetism Does Not Exist in Classical Physics

What is Van Leeuwen's Theorem?

Van Leeuwen's Theorem is a fundamental principle in classical physics that states that diamagnetism, the property of a material to be repelled by a magnetic field, does not exist in classical physics. It was first proven by Dutch physicist Hendrik van Leeuwen in 1919.

What is the significance of this theorem?

This theorem has significant implications for our understanding of magnetism and materials. It helps to explain why some materials, such as copper and gold, are not affected by magnetic fields in classical physics. It also plays a role in the development of quantum mechanics, where diamagnetism is observed in materials.

How was the theorem proven?

Van Leeuwen's Theorem was proven using statistical mechanics. By considering the thermal motion of electrons in a material, van Leeuwen showed that there can be no net magnetization in a classical system. This means that diamagnetism cannot exist in classical physics.

Are there any exceptions to this theorem?

No, there are no exceptions to Van Leeuwen's Theorem in classical physics. It is a fundamental principle that applies to all materials and systems in classical mechanics.

Has this theorem been tested and confirmed?

Yes, Van Leeuwen's Theorem has been extensively tested and confirmed through experiments and calculations. It is widely accepted as a fundamental principle in classical physics.

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