Heizenberg's Uncertainty Principle

 Nobel laureate Weinberg (Ref. 7 of the English translation of the original paper by Heisenberg's paper)  has written as follows: ‘If the reader is mystified at what Heisenberg was doing, he or she is not alone. I have tried several times to read the paper that Heisenberg wrote on returning from Heligoland, and, although I think I understand quantum mechanics, I have never understood Heisenberg’s motivations for the mathematical steps in his paper. Theoretical physicists in their most successful work tend to play one of two roles: they are either sages or magicians....It is usually not difficult to understand the papers of sage-physicists, but the papers of magicianphysicists are often incomprehensible. In that sense, Heisenberg’s 1925 paper was pure magic."

So, it is very difficult to understand the Uncertainty principle from original paper. The paper in the above link try to give the method that Heisenberg may have used. 

Topology

Wikipedia article on topology  says:

• "Topology is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing."
• "Topology developed as a field of study out of geometry and set theory, through analysis of concepts such as space, dimension, and transformation"

Spend some solid amount of time to get a clear picture on Topology. 

Topology is a rich field and has many sub-fields. 

• General topology, also called point-set topology, establishes the foundational aspects of topology and investigates properties of topological spaces and concepts inherent to topological spaces. It defines the basic notions used in all other branches of topology (including concepts like compactness and connectedness).
• Algebraic topology tries to measure degrees of connectivity using algebraic constructs such as homology and homotopy groups.
• Differential topology is the field dealing with differentiable functions on differentiable manifolds. It is closely related to differential geometry and together they make up the geometric theory of differentiable manifolds.
• Geometric topology primarily studies manifolds and their embeddings (placements) in other manifolds. A particularly active area is low-dimensional topology, which studies manifolds of four or fewer dimensions. This includes knot theory, the study of mathematical knots.

(This page need updates. Please come back later or go through Wikipedia article or other sources)

The pair of words that always confuse for many people

There are some words and phrases which is always confusing to us (or at least for me 😊).

Here is some of the list. It may take a while to understand the difference between them.

You can comment below to add more similar words.

• centripetal force and centrifugal force
• cpu and core
• affect and effect
• principal and principle
• whether and weather
• potential and potential energy

Links to Colloquium around the world

Colloquium is an excellent forum for updating and to get many ideas for solving problems and also to find out interdisciplinary problems. Almost all prominent universities conduct weekly colloquium. Here, I try to list them as I come across.

Following is the lists of colloquium around the world (Physics and Mathematics). I provide links for the university pages where videos/video-links are available.

• The Zurich Physics Colloquium (ETH Z$\ddot{u}$rich)
• Sommerfeld Theory Colloquium (Ludwig Maximilian University of Munich. A complete list of all the lectures, schools and workshop from Arnold Sommerfield center may be accessed from this page)

(This page will be updated whenever possible. Thanks for visiting this page.)

Linux tips basic comments (ls, mv, cp)

To rename a directory 

mv /home/user/oldname /home/user/newname

Formalism and Interpretation of Quantum Mechanics

We saw that there are many formalism for classical mechanics. Similarly, there are many formalism for quantum mechanics. Quantum mechanics is one of the successful theories that describe our nature. Albeit its success and many formalism, the interpretation of quantum mechanics is settled yet.

Different formalism of Quantum Mechanics are

1. Heisenberg 
2. Interaction 
3. Matrix  
4. Phase-space 
5. Schrödinger 
6. Sum-over-histories (path integral)
7. PT-symmetric Quanum Mechanics (Prof. Carl M Bender)
8. Ryu Sasaki formalism

The different interpretations of Quantum Mechanics are

1. Consistent histories 
2. Copenhagen interpretation
3. de Broglie–Bohm theory
4. Ensemble interpretation 
5. Hidden-variable theory 
6. Many-worlds interpretation
7. Objective collapse theory
8. Quantum Bayesianism
9. Quantum logic 
10. Relational quantum mechanics
11. Stochastic quantum mechanics
12. Scale relativity 
13. Transactional interpretation

Different formalism of Classical Mechanics

The study of mechanics which started with Galileo now rich in the sense that many different formalism are available. Here are the different formalism of Classical Mechanics.

• Newton's laws of motion
• Analytical mechanics
• Lagrangian mechanics
• Hamiltonian mechanics
• Routhian mechanics
• Hamilton–Jacobi equation
• Appell's equation of motion
• Udwadia–Kalaba equation
• Koopman–von Neumann mechanics

Here is the Wikipedia article to know more about Lagrangian mechanics. On the top right corner of the page, links are given for the different formalism (listed above)

(will be updated)

sudo apt auto-remove

What is the use of following command?

sudo apt auto-remove

This automatically removes unwanted packages from the linux distro.

Latex Tips (2)

How to add double dots on a character? For example, In the name Schrodinger, the correct writing would be a double dot on the letter "o". How this can be done?

To do this,

use \ddot{o}

This will give you ${\ddot{\text{o}}}$

In the name Schrodinger, use above syntax and you will get Schr${\ddot{\text{o}}}$dinger which you wanted.

Using Latex in blogspot

To add equations in the blogspot, there is a code provided by Prof. Matthew Leingang in Tex Stack Exchange site.

Click here to visit the Tex Stack Exchange page and answer.

Basically, what you need to do is

• Go to Theme
• Edit HTML
• Paste following code below <head> 
• Then save.

Now, you can use $LaTeX$ in posts.

<script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js">
MathJax.Hub.Config({
 extensions: ["tex2jax.js","TeX/AMSmath.js","TeX/AMSsymbols.js"],
 jax: ["input/TeX", "output/HTML-CSS"],
 tex2jax: {
     inlineMath: [ ['$','$'], ["\\(","\\)"] ],
     displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
 },
 "HTML-CSS": { availableFonts: ["TeX"] }
});
</script>