Nuclear and particle physics through Scilab. More…

# Category Archives: quantum mechanics

# Understanding Nuclear Physics through SCILAB.

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LIGO in India? You must be kidding …
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I was pleasantly surprised that this experiment is slated to come up in India, yes, with a whopping 250 million dollars investment into science in India is perhaps the only 2nd instance of massive science euphoria.

And they are both directly or immediately so, in my field of research, although the first one INO isn’t seeming to be coming of age, while collaborations and Physics and engineering as such have been extensively laid out in the ground, the lab the much coveted international particle physics lab that is, hasn’t come.

(Surprise me, if work has already begun in Madurai, we have been struck by paranoia of environment so much that the elephants have the right of way more than the most innocuous science commies out there, pardon me, that’s a pun, no disrespect to elephants, no offense to commies.) More…

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What happens when squirrels do not move.
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Stationary state and squirrels !

Okay so the squirrel isn’t moving around so much, giving a fuzzy image. We can call the instant during which the squirrel wasn’t moving akin to a “gross” stationary state.

But why is the railing of window fuzzy? It isn’t moving !

Diffraction.

Due to diffraction enough light is coming from the other side of the iron bar, to enable us to see whats there. That quadrangle is diffracting the light. But why its fuzzy?

Diffraction is by its own very nature even though purely classical in many sense, fuzzy towards energy if time window is small. [due to energy vs time uncertainty]

That is, full energy cycle isn’t available, because a small time window is chosen. If you time-lapse the photograph, diffraction will become quite insignificant. Although it might still be there depending on details. More…

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Waves, particles and Einstein !
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Waves are something that have no mass and move at the maximum speed, mass m = 0. speed c = 1. So whats their momentum? p = m.v = 0? Right?

No. For pure waves; momentum does not come from mass. It comes only from motion.

(pure wave; they do not have mass)

For matter waves, on the other hand, momentum comes in two ways, mass as well as motion.

(impure, now they have mass)

Albert Einstein recognized this fact and derived his relation; $latex E = \sqrt {(pc)^2+(mc^2)^2}$

This relation is called as Einstein’s relativistic equation, also Einstein’s mass-energy relation. But more appropriately mass-energy-momentum relation.

Let us consider E as the hypotenuse, p and m; as base or perpendicular as is your choice.

triangle_copyThen $latex E = \sqrt {(pc)^2+(mc^2)^2}$ is Pythagoras Theorem; when p is momentum and m is mass.

For pure waves such as photon … the quanta of light, m = 0.

Hence the Pythagorean Triangle is now one, where the mass side is arbitrary small. Thus E = p. More…

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What happens when cows move rapidly !
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Cows not moving and moving fast. How does this difference impact the image in a modern digital camera?

Honestly I haven’t checked it with old day manual camera neither do I remember what impact motion brings into mages taken by such, eg does anyone remember when he/she took a picture of a friend standing in a platform and a train was coming, what happened to the image due to such motion?

Do you see where the fuzziness coming from, in the pictures, where the cows are moving?

Its coming from the relative motion between “objects being imaged” (cows and grass etc) and equipment of imaging (camera). This fuzziness is quite small when they are both still (the object and camera, wrt each other). More…

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New forms of Uncertainty Relationships in Quantum Mechanics.
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ΔE.Δt ~ h

Δp.Δx ~ h

ΔL.Δθ ~ h

* Shouldn’t the constant above be ℏ/2 ? Let us first clear up some air of confusion.

The above relations are kind of vague even though look like canonically powerful ways to represent the formal concepts of the Heisenberg Uncertainty relationships. I have myself confused with these at times … with the added degree of confusion coming from h or h-cross?

But there is nothing to be ashamed of, if one makes such mistakes.

Does ℏ/2 come due to normalization of wave function or discrepancy in definition? eg do they come because variance (ΔE, Δx) and standard deviation (σx , σH ). More…