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Notes on topics in scienceTue, 28 Mar 2017 05:56:01 +0000hourly1Comment on Translational invariance in quantum mechanics by Vikrant Chaudhary
http://www.physicspages.com/2017/03/27/translational-invariance-in-quantum-mechanics/#comment-202575
Tue, 28 Mar 2017 05:56:01 +0000http://www.physicspages.com/?p=14401#comment-202575I realy enjoyed reading this article. Great work!
]]>Comment on The classical limit of quantum mechanics; Ehrenfest’s theorem by Translational invariance in quantum mechanics | Physics pages
http://www.physicspages.com/2017/01/16/the-classical-limit-of-quantum-mechanics-ehrenfests-theorem/#comment-202541
Mon, 27 Mar 2017 16:31:09 +0000http://www.physicspages.com/?p=14185#comment-202541[…] of the commutator must be zero (the derivation is done in Shankar’s eqn 11.2.15). Using Ehrenfest’s theorem we then find that the expectation value , so that the expectation value of is conserved over […]
]]>Comment on Passive, regular and active transformations. Invariance of the Hamiltonian and generators of transformations by Translational invariance in quantum mechanics | Physics pages
http://www.physicspages.com/2016/12/11/passive-regular-and-active-transformations-invariance-of-the-hamiltonian-and-generators-of-transformations/#comment-202540
Mon, 27 Mar 2017 16:28:23 +0000http://www.physicspages.com/?p=14065#comment-202540[…] classical mechanics, we’ve seen that if a dynamical variable is used to generate a transformation of the variables and (the […]
]]>Comment on Manifolds, curves and surfaces by José Victor
http://www.physicspages.com/2012/12/21/manifolds-curves-and-surfaces/#comment-202516
Mon, 27 Mar 2017 09:20:49 +0000http://physicspages.com/?p=1672#comment-202516Dear Teacher, this introductory explanation of space, manifold and its characterization, is the simplest, most objective and precise I have ever read.
Congratulations.

JVictor
Recife, Pernambuco, Brasil

]]>Comment on Toroidal solenoid with a gap by gwrowe
http://www.physicspages.com/2013/06/30/toroidal-solenoid-with-a-gap/#comment-202511
Mon, 27 Mar 2017 08:25:32 +0000http://physicspages.com/?p=3191#comment-202511Follow the link “centre of such a loop” just before eqn 8.
]]>Comment on Schroeder – Thermal Physics problems by Patrick
http://www.physicspages.com/index-physics-thermal-statistical/schroeder-thermal-physics-problems/#comment-202498
Mon, 27 Mar 2017 00:56:59 +0000http://physicspages.com/?page_id=5343#comment-202498Original Gangster. Don’t worry, it’s a compliment!
]]>Comment on Toroidal solenoid with a gap by Justin
http://www.physicspages.com/2013/06/30/toroidal-solenoid-with-a-gap/#comment-202497
Mon, 27 Mar 2017 00:55:26 +0000http://physicspages.com/?p=3191#comment-202497Magnetic field of the loop, not torus*
]]>Comment on Toroidal solenoid with a gap by Justin
http://www.physicspages.com/2013/06/30/toroidal-solenoid-with-a-gap/#comment-202496
Mon, 27 Mar 2017 00:55:05 +0000http://physicspages.com/?p=3191#comment-202496How exactly was the magnetic field of the torus derived? I am trying to do a similar problem, except with a thin loop instead of a square one.
]]>Comment on The adiabatic approximation in quantum mechanics by gwrowe
http://www.physicspages.com/2014/12/04/the-adiabatic-approximation-in-quantum-mechanics/#comment-202453
Sun, 26 Mar 2017 10:57:36 +0000http://physicspages.com/?p=5276#comment-202453The functions defined in eqn 6 form an orthonormal basis for the Hilbert space, so any function defined on that space can be written as a series using these functions. That’s what is done in eqn 10. In eqn 15, we are specifying the initial state of the system as the function , and we know that can be written as a series over (with ) as given in eqn 10. This series will contain an infinite number of terms (not just ), with the coefficients given by eqn 17. The eigenfunctions of a static square well aren’t the same as those of an expanding square well, so it’s not correct to say that only the term is present in 10 when the system is in the ground state of a static square well. It’s probably easier just to ignore the physics and regard eqn 10 as a purely mathematical expression, where a function is expanded in a series of basis functions.
]]>Comment on The adiabatic approximation in quantum mechanics by Joshua Brown
http://www.physicspages.com/2014/12/04/the-adiabatic-approximation-in-quantum-mechanics/#comment-202398
Sat, 25 Mar 2017 15:14:32 +0000http://physicspages.com/?p=5276#comment-202398I suppose my confusion starts then with Eq 10 where you have defined Psi. If I plug Eq 6 into 10 and assume that all the coefficients are 0 except for the ground state which I believe should be 1 I end up with.

Phi = sqrt(2/a) * sin( pi x / a) exp( i ( m v x^2 / ( 2 hbar a))

Are we assuming that v is 0 at this point? If so I guess that would make the exponent disappear.