Very specific Q's on the P and H operators

In summary: In 1926, in "Annalen der Physik", Erwin Schrödinger published 5 articles: 1) On the application of the mathematical theory of waves to the problems of physical optics 2) On the application of the mathematical theory of waves to the problems of physical acoustics 3) On the application of the mathematical theory of waves to the problems of physical Electricity and magnetism 4) On the quantum-mechanical description of the radiation from an atom5) On the origin and meaning of the mathematical theory of waves.Erwin Schrödinger developed the Schrödinger equation, a mathematical model that describes the behavior of particles in an environment.
  • #1
sifeddin
30
0
I ask very specific Questions on the P momentum operator and the H energy operator:
Who the first gave them their commonly known spatial and timporal differential form? Was he really Schrodinger? On what basis they are so? Is they depend on the classical mechanics correspondance principle/postulate?
Finally I like to get the reference to whatever you knowledgeable poeple of QM reply to me.
 
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  • #2
sifeddin said:
Who the first gave them their commonly known spatial and timporal differential form?

ERWIN SCHRÖDINGER.

sifeddin said:
Was he really Schrodinger?

No,he was Schrödinger.

sifeddin said:
On what basis they are so?

Because they correctly repreduce Schrödinger's equation.

sifeddin said:
Is they depend on the classical mechanics correspondance principle/postulate?

The principle of correspondance was formulated by N.Bohr,after having seen the results obtained by Schrödinger and,generall,QM.

sifeddin said:
Finally I like to get the reference to whatever you knowledgeable poeple of QM reply to me.

In 1926,in "Annalen der Physik",Erwin Schrödinger published 5 articles (though Weinberg* mentions only 4):
*Vol.79,page 361.
*Vol.79,page 489.
*Vol.79,page 734 (not mentioned by Weinberg*,but part of the footnote on the first page of (**)).
*Vol.80,page 437.
*Vol.81,page 109 (containing in the 6-th section the relativistic Schrödinger equation,according to Weinberg*).

The general ideas and results of these articles (less the relativistic equation) were published by Erwin Schrödinger in English in the American journal:
"The Physical Review",Second Series,Vol.28,No.6,page 1049,Dec.1926 (**)

In this article the correspondence:
[tex] p_{x}\rightarrow \frac{h}{2\pi}\frac{\partial \psi}{\partial x} ,... [/tex]

is found in section #7,page 1064 (of the Journal),in the text between formulas #22 and #23.

And in formula #23 he gives the general classical Hamiltonian as a quadratic form of momenta + the potential energy and then applies the same rule to the classical momenta.
Equation #26 is the generalization of equation #16,the latter giving the time-independent SE for one particle in the potential field V...

Daniel.

-----------------------------------------------------------
* Steven Weinberg,"The Quantum Theory of Fields",CUP,1995,Volume 1,page 40-41.
 
  • #3
Can anyone help me find an english electronic version of the Annalen der Physik "five" papers
 
  • #4
help! Again:
Can anyone help me find an english electronic version of the Annalen der Physik "five" papers
 

1. What is the difference between the P and H operators?

The P operator, also known as the momentum operator, is used to determine the momentum of a particle in quantum mechanics. It is represented by the symbol "p" and is defined as the product of the mass of the particle and its velocity. The H operator, also known as the Hamiltonian operator, is used to determine the total energy of a particle in quantum mechanics. It is represented by the symbol "H" and is defined as the sum of the kinetic and potential energies of the particle.

2. How are the P and H operators related to Heisenberg's uncertainty principle?

The Heisenberg's uncertainty principle states that it is impossible to know the exact position and momentum of a particle simultaneously. This principle is related to the P and H operators as the P operator is used to determine the momentum of a particle, while the H operator is used to determine the position of a particle. Therefore, the uncertainty principle is a result of the mathematical properties of the P and H operators.

3. Are the P and H operators Hermitian?

Yes, both the P and H operators are Hermitian. This means that they are self-adjoint and satisfy the property of Hermiticity, which states that the transpose of the operator is equal to its conjugate. In quantum mechanics, Hermiticity is important as it ensures that the operators have real eigenvalues and the corresponding eigenvectors are orthogonal to each other.

4. How are the P and H operators used in quantum mechanics?

The P and H operators are fundamental mathematical operators used in quantum mechanics to describe the behavior of particles at the atomic and subatomic level. They are used to determine the momentum and energy of a particle, which are essential for understanding the behavior of particles in quantum systems. The eigenvalues and eigenvectors of these operators are used to solve the Schrödinger equation and predict the behavior of particles in various physical systems.

5. Can the P and H operators be used in classical mechanics?

No, the P and H operators are specific to quantum mechanics and cannot be used in classical mechanics. This is because classical mechanics is based on deterministic principles, where the position and momentum of a particle can be known precisely at any given time. In contrast, quantum mechanics is based on probabilistic principles, where the P and H operators are used to calculate the probability of a particle being in a certain state at a given time.

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