physicsfromthebottomup.blogspot.com
Exploring the Mountain: The Wave Function 05
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Noli turbare circulos meos. Thursday, May 29, 2014. The Wave Function 05. Mdash; 1.6. The Uncertainty Principle —. Imagine now that, instead of just producing one jerk, you continuously wave the rope so that you end up producing a standing wave. In this case the wavelength is perfectly defined, since this a phenomenon that is periodic, but the wave position loses its meaning. Quantum mechanics, as we'll see in later posts, asks for a particle description that is given in terms of wave packets. In a more ...
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Exploring the Mountain: What is this all about?
http://physicsfromthebottomup.blogspot.com/2009/02/plan.html
Noli turbare circulos meos. Thursday, February 12, 2009. What is this all about? On my other blog. On Wordpress I have a pretty clear and definite plan. On that blog I'll write up my class notes, and other resources, with the goal of re-studying and having a stronger and more united grasp of physics. Here I'll just post meta-questions. I mean such questions has: "Why is it necessary to build on an axiomatic basis the real numbers? Why are we also presenting physics in an axiomatic way? That allows a ....
physicsfromthebottomup.blogspot.com
Exploring the Mountain: The Wave Function Exercises 01
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Noli turbare circulos meos. Friday, March 28, 2014. The Wave Function Exercises 01. J 2 =1/N sum j 2N(J)= dfrac{6434}{14}=459.6}$. Calculating for each $ { Delta j}$. Delta j=j- j }$. Hence for the variance it follows. Sigma 2=1/N sum ( Delta j) 2N(j)= dfrac{260}{14}=18.6}$. Hence the standard deviation is. Displaystyle sigma = sqrt{18.6}=4.3$. Sigma 2= j 2 - j 2=459.6-441=18.6}$. And for the standard deviation it is. Displaystyle sigma = sqrt{18.6}=4.3$. Hence for the digits it is. The plot for the prob...
physicsfromthebottomup.blogspot.com
Exploring the Mountain: Newtonian Mechanics 01
http://physicsfromthebottomup.blogspot.com/2014/02/newtonian-mechanics-01.html
Noli turbare circulos meos. Thursday, February 27, 2014. 8212; 2. Initial Considerations —. Without being too far away from the truth one can say that modern Fundamental Physics rests on these three conceptions. The concept of field. The theory of relativity. The concept of field is essential to all of our future discussion hence we'll define it right away:. Field is an mathematical structure with a defined value in a given set of points. A field is said to be a scalar field when it assumes scalar values.
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Exploring the Mountain: The Wave Function 02
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Noli turbare circulos meos. Friday, March 28, 2014. The Wave Function 02. 8212; 1.3. Probability —. In the previous post. We were introduced to the Schrodinger equation (equation 1. Stated Born's interpretation of what is the physical meaning of the wave function and took a little glimpse into some philosophical positions one might have regarding Quantum Mechanics. 8212; 1.3.1. Discrete variables —. One person has 14 years. One person has 15 years. Three people have 16 years. Two people 22 years. The pro...
physicsfromthebottomup.blogspot.com
Exploring the Mountain: Matrices, Scalars, Vectors and Vector Calculus 01
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Noli turbare circulos meos. Monday, February 24, 2014. Matrices, Scalars, Vectors and Vector Calculus 01. Let us imagine that we have a system of coordinates $ {S} $ and a system of coordinates $ {S'} $ that is rotated relatively to $ {S} $. Let us consider a point $ {P} $ that has coordinates $ {(x 1,x 2,x 3)} $ on $ {S} $ and coordinates $ {(x' 1,x' 2,x' 3)} $ on $ {S'} $. In general it is obvious that $ {x' 1=x' 1(x 1,x 2,x 3)} $, $ {x' 2=x' 2(x 1,x 2,x 3)} $ and that $ {x' 3=x' 3(x 1,x 2,x 3)} $.
physicsfromthebottomup.blogspot.com
Exploring the Mountain: July 2014
http://physicsfromthebottomup.blogspot.com/2014_07_01_archive.html
Noli turbare circulos meos. Wednesday, July 23, 2014. Time-independent Schrodinger equation 02. Mdash; 2. The infinite square well —. Imagine a situation where a projectile in confined to a one dimensional movement and bounces off two infinitely rigid walls while conserving kinetic energy. This situation can be modeled by the following potential:. Displaystyle f(x) = begin{cases} 0 quad 0 leq x leq a infty quad mathrm{otherwise} end{cases}$. Displaystyle - frac{ hbar 2}{2m} frac{d 2 psi}{dx 2}=E psi $.
physicsfromthebottomup.blogspot.com
Exploring the Mountain: Mathematical trick in Statistical Physics
http://physicsfromthebottomup.blogspot.com/2011/04/mathematical-trick-in-statistical.html
Noli turbare circulos meos. Wednesday, April 13, 2011. Mathematical trick in Statistical Physics. The other day I was looking into some Statistical Physics and ended up doing an exercise that was kinda cute. The exercise in question is on Mandl's Statistical Physics, Second Edition page 66. The first time I did the exercise I did it the normal way, but then I noticed something that ended up simplifying my calculations and here I am posting it. A system has three energy levels. Displaystyle begin{array}{r...
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Exploring the Mountain: The Quantum Gang
http://physicsfromthebottomup.blogspot.com/2009/02/the-quantum-gang.html
Noli turbare circulos meos. Sunday, February 1, 2009. Which is, hands down, the best introductory book on Quantum Mechanics) doing almost all of the exercises, discussing almost all of the finer details, and getting a real understanding of a truly interesting and important topic. Even though the book is pretty much self contained, Physics wise, one does need a little bit of minimum baggage. Some suggestions, for this minimum baggage, may be:. Classical Dynamics of Particles and Systems. Time-independent ...
physicsfromthebottomup.blogspot.com
Exploring the Mountain: May 2014
http://physicsfromthebottomup.blogspot.com/2014_05_01_archive.html
Noli turbare circulos meos. Saturday, May 31, 2014. Time-independent Schrodinger equation 01. 8212; 1. Stationary states —. In the previous posts we've normalized wave functions, we've calculated expectation values of momenta and positions but never at any point we've made a quite logical question:. How does one calculate the wave function in the first place? The answer to that question obviously is:. You have to solve the Schroedinger equation. The Schroedinger equation is. Calculating the appropriate d...
