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	[NOTES/QM-06002] Postulates of Quantum Mechanics Node id: 5454page We list the postulates of the Hilbert space formulation of quantum mechanics. These are Description of states on quantum systems.The states are represented by vectors in a complex vector space Hermitian operators as observables.The observables are represented by hermitian operators This postulate connects theory with experiments by giving rules for computation of probabilities. Canonical quantizationThis postulate gives the basic commutation relations and makes actual computation possible. Law for time evolutionThis postulate plays the same role for quantum mechanics as "Newton's Second Law" does for Newtonian mechanics Symmetrization postulate.This is the spin statistics connection giving symmetry properties of wave functions under exchange of two identical particles.	kapoor	24-03-18 13:03:27	n
	[NOTES/QM-06004] A Discussion of The Third Postulate of Quantum Mechanics Node id: 5877page The third postulate of quantum mechanics is discussed in detail.	kapoor	24-03-18 13:03:18	n
	[NOTES/QM-06001] Why Start with Postulates? Node id: 6104page Many concepts of classical mechanics have to be revised or given up completely. Also in quantum mechanics many new concepts, such as quantization of dynamical variables, appear. In order to understand the structure of quantum mechanics and its applications well, it si recommended that teaching and learning of quantum mechanics should begin with the postulates.	kapoor	24-03-18 13:03:12	n
	[NOTES/CM-02003] From Newton's EOM to Euler Lagrange EOM Node id: 6037page Euler Lagrange equations are obtained using Newton's laws and D' Alembert's principle. $\newcommand{\dd}[2][]{\frac{d#1}{d#2}}\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}$	kapoor	24-03-15 06:03:32	n
	[NOTES/CM-02001] Limitations of Newtonian Mechanics Node id: 6100page Some limitations of Newtonian mechanics are pointed out.	kapoor	24-03-15 04:03:24	n
	[NOTES/EM-07017] Magnetic Moment of a System of Point Particles Node id: 5990page The magnetic moment for a point particle is shown to be related to the angular momentum \(\ell\) and is given by \begin{equation} \vec{m} = \frac{q}{2M}\vec{\ell} \end{equation}	kapoor	24-03-12 23:03:46	n
	[LECS/EM-07005] Currents in Magnetic Field Node id: 6094page	kapoor	24-03-11 17:03:21	n
	[NOTES/QFT-01001] Examples of Classical Fields Node id: 6097page After recalling the analytical dynamics briefly, several examples of systems with infinite degrees of freed are given.	kapoor	24-03-10 09:03:01	n
	[NOTES/EM-07006]-Lorentz Force on a Current Distribution Node id: 5711page Starting from Lorentz force per unit volume on a current carrying conductor due to magnetic field is shown to be \(\vec{j}\times\vec{B}\)	AK-47	24-03-05 09:03:16	n
	[NOTES/EM-07005]-Torque on a Current Carrying Loop Node id: 5710page An expression for torque on a current carrying loop in magnetic field is obtained. It is shown that the torque is given by \(\vec{\tau}=\vec{m}\times\vec{B}\), where \(\vec{m}\) is the magnetic moment of the loop. For a planar loop\(\|\vec{m}\|=\) current \(\times\) area.	AK-47	24-03-05 09:03:22	n
	[LECS/EM-07007] Magnetic Field of Localized Currents Node id: 6096page	kapoor	24-03-04 22:03:42	n
	[LECS/EM-07006] Vector Potential Node id: 6095page	kapoor	24-03-04 22:03:01	n
	[LECS/EM-07003] Biot-Savart Law and Maxwell's Equations Node id: 6092page	kapoor	24-03-04 22:03:56	n
	[LECS/EM-07004] Magnetic Field of Currents Node id: 6093page	kapoor	24-03-04 22:03:33	n
	2. Mathematical Preparation Node id: 6091page	kapoor	24-03-03 10:03:11	n
	1. Current Density and Current Conservation* Node id: 6056page	kapoor	24-03-03 10:03:44	n
	[DOC/ToDo] List of ToDos Node id: 6090page This page contains a list of todos which have to be done at a later date. For example creation of hyperlinks to pages that will be created later.	kapoor	24-03-03 06:03:42	n
	[Doc, Log, Info, Help,...] Documentaion of Proofs Content Node id: 6085collection	kapoor	24-03-03 06:03:50	n
	1.1 The Structure of Physical Theories --- Lectures given at Hyd Univ -2024 Refresher Course Node id: 6059page	kapoor	24-03-02 22:03:31	n
	[NOTES/EM-07013] Conservtion of Electromagnetic Field Momentum.* Node id: 5919page The equation of continuity appears in different branches of physics. It represents a local conservation law. In order to be consistent with requirement if special relativity every conserved quantity must come with a current which gives the flow of the conserved quantity across a surface and the two must obey equation of continuity. Taking the example of momentum conservation, we briefly discuss the interpretation of stress tensor giving flow of momentum per unit time as a surface integral. The surface integral, in turn, gives the force on the surface. $\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}} \newcommand{\dd}[2][]{\frac{d#1}{d#2}}$	kapoor	24-03-02 11:03:19	n

We list the postulates of the Hilbert space formulation of quantum mechanics. These are

Description of states on quantum systems.The states are represented by vectors in a complex vector space
Hermitian operators as observables.The observables are represented by hermitian operators
This postulate connects theory with experiments by giving rules for computation of probabilities.
Canonical quantizationThis postulate gives the basic commutation relations and makes actual computation possible.
Law for time evolutionThis postulate plays the same role for quantum mechanics as "Newton's Second Law" does for Newtonian mechanics
Symmetrization postulate.This is the spin statistics connection giving symmetry properties of wave functions under exchange of two identical particles.

The third postulate of quantum mechanics is discussed in detail.

Many concepts of classical mechanics have to be revised or given up completely. Also in quantum mechanics many new concepts, such as quantization of dynamical variables, appear. In order to understand the structure of quantum mechanics and its applications well, it si recommended that teaching and learning of quantum mechanics should begin with the postulates.

Euler Lagrange equations are obtained using Newton's laws and D' Alembert's principle.
$\newcommand{\dd}[2][]{\frac{d#1}{d#2}}\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}$

Some limitations of Newtonian mechanics are pointed out.

The magnetic moment for a point particle is shown to be related to the angular momentum $\ell$ and is given by
\begin{equation}
\vec{m} =
\frac{q}{2M}\vec{\ell}
\end{equation}

After recalling the analytical dynamics briefly, several examples of systems with infinite degrees of freed are given.

Starting from Lorentz force per unit volume on a current carrying conductor due to magnetic field is shown to be $\vec{j}\times\vec{B}$

An expression for torque on a current carrying loop in magnetic field is obtained. It is shown that the torque is given by $\vec{\tau}=\vec{m}\times\vec{B}$, where $\vec{m}$ is the magnetic moment of the loop. For a planar loop$|\vec{m}|=$ current $\times$ area.

This page contains a list of todos which have to be done at a later date.
For example creation of hyperlinks to pages that will be created later.

The equation of continuity appears in different branches of physics. It represents a local conservation law. In order to be consistent with requirement if special relativity every conserved quantity must come with a current which gives the flow of the conserved quantity across a surface and the two must obey equation of continuity. Taking the example of momentum conservation, we briefly discuss the interpretation of stress tensor giving flow of momentum per unit time as a surface integral. The surface integral, in turn, gives the force on the surface.

$\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}} \newcommand{\dd}[2][]{\frac{d#1}{d#2}}$

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[NOTES/QM-06002] Postulates of Quantum Mechanics

[NOTES/QM-06004] A Discussion of The Third Postulate of Quantum Mechanics

[NOTES/QM-06001] Why Start with Postulates?

[NOTES/CM-02003] From Newton's EOM to Euler Lagrange EOM

[NOTES/CM-02001] Limitations of Newtonian Mechanics

[NOTES/EM-07017] Magnetic Moment of a System of Point Particles

[LECS/EM-07005] Currents in Magnetic Field

[NOTES/QFT-01001] Examples of Classical Fields

[NOTES/EM-07006]-Lorentz Force on a Current Distribution

[NOTES/EM-07005]-Torque on a Current Carrying Loop

[LECS/EM-07007] Magnetic Field of Localized Currents

[LECS/EM-07006] Vector Potential

[LECS/EM-07003] Biot-Savart Law and Maxwell's Equations

[LECS/EM-07004] Magnetic Field of Currents

2. Mathematical Preparation

1. Current Density and Current Conservation*

[DOC/ToDo] List of ToDos

[Doc, Log, Info, Help,...] Documentaion of Proofs Content

1.1 The Structure of Physical Theories --- Lectures given at Hyd Univ -2024 Refresher Course

[NOTES/EM-07013] Conservtion of Electromagnetic Field Momentum.*

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