Pauli's Wave Mechanics text. h vs. hbar

In summary, the book "Wave mechanics" by Pauli uses h for hbar, which represents Planck's constant divided by 2 pi, and this has been the case in both older and newer literature. The definitions of these constants are not in a state of flux. While there may be examples where h is used instead of hbar or vice versa, they are rare and usually involve ignoring factors of 2 pi. Additionally, there may be discrepancies in formulas when using CGS electromagnetic units compared to SI units.
  • #1
Peeter
305
3
In this little Dover book "Wave mechanics", by Pauli, it appears to use h for hbar, and includes a footnote right on the very first page

"1. In these lectures we use the symbol h to denote the quantity 1.05 x 10^-34 joule.sec. In the older literature this quantity was usually denoted by [itex]\hbar[/itex]"

However, this is what I've seen in the newer literature too. Are the definitions of these constants in a state of flux?
 
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  • #2
No, [tex] \hbar [/tex] should always represent Planck's constant divided by 2 pi in modern text.
I don't think I've ever encountered an example where someone has specifically used [tex]h[/tex] instead of [tex]\hbar[/tex] or vice versa. There are, however, examples of texts where the author is ex. ignoring factors of 2pi etc simply because they are interested in order-of-magnitude estimates and factors of the order of one does one matter.

Also, note that formulas where CGS electromagnetic units are used often differ by a factor of 2pi compared to the equivalent formulas in SI (and there are plenty of examples of papers where the authors have added/removed a 2pi too many).
 

1. What is the difference between h and hbar in Pauli's Wave Mechanics text?

H and hbar both represent the Planck constant, which is a fundamental constant in quantum mechanics. However, hbar (ħ) is the reduced Planck constant and is equal to h divided by 2π. It is often used in equations involving angular momentum and is more convenient than using the full value of h.

2. Why is the Planck constant important in Pauli's Wave Mechanics text?

The Planck constant is important because it relates the energy of a quantum system to its frequency. In Pauli's Wave Mechanics text, it is used to describe the behavior of particles on a quantum level, such as the energy levels of electrons in an atom.

3. How does hbar relate to the uncertainty principle in Pauli's Wave Mechanics text?

The uncertainty principle states that it is impossible to know both the exact position and momentum of a particle at the same time. Hbar is a fundamental part of the uncertainty principle, as it is used to calculate the uncertainty in a particle's position or momentum.

4. Is hbar the same as the Planck constant in Pauli's Wave Mechanics text?

No, hbar is not the same as the Planck constant. As mentioned before, hbar is the reduced version of the Planck constant and is equal to h divided by 2π.

5. Can you give an example of an equation in Pauli's Wave Mechanics text that uses hbar?

One example of an equation that uses hbar is the Schrödinger equation, which describes the behavior of a quantum system. The equation includes hbar in the form of the Hamiltonian operator, which relates the energy of the system to its wave function.

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