THE LEAST-ACTION PRINCIPLE & QUANTUM MECHANICS. Vu Huy Toan (Vietnam) firstname.lastname@example.org. LEAST ACTION PRINCIPLE AND QUANTUM MECHANICS. I. INTRODUCTION . II. BASIS CONCEPTS. 1. Effect of and action among physical objects 2. Least effect and least action.
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Vu Huy Toan (Vietnam)
II. BASIS CONCEPTS.
1. Effect of and action among physical objects
2. Least effect and least action.
III. LEAST ACTION PRINCIPLE (LAP).
IV. CONSIDERATION OF SOME PHENOMENA ON THE BASIS OF LAP.
1. The particle movement under the action of a force.
2. Wave property of fundamental particles.
3. Movement orbit quantization of electron in atom.
Return to the classical mechanics…
As recognized above, there cannot be any effect smaller than the h leasteffect value. This also means that H effect function pursuant to (4) is not continuous and it can only be the multiple number of h:
H = nh, (n = 1, 2, 3,…) (8)
On the other hand, any occurring physical processes are associated with the energy exchange. That exchange occurs on every small portion. Thus, corresponding to the least effect h is the least action d.
h = d. (9)
"For a physical object to change its energy state, the action on it can not be smaller than the least action".
D = 2E(t)dt d = h/ (10)
If E(t) = E = const and = 1 then:
D = 2E(t1- t0) = 2Et h (11)
- In case the living time of the given object is equal to τ1, ∆t τ1;
- In case the possible time interval for the two objects to exchange their energy is equal to τ2, ∆t τ2 ;
- In case the object under the action is moving in the period of T, ∆t T
1.The movement of PO under the action of a force
2.Wave property of fundamental particles
3. Movementorbit quantization of electron in atom
e-ΔE E1(t)+ΔE1 f1(t)+Δf1
vα = vncosαon
1. According to LAP, the fundamental particle can merely move in “jerky steps” varying its velocity along with each step, but not in regularly increasing or decreasing manner.
2. The “physical wave” does not exist! The particle just has “wave-like manifestation”, but not “waveproperty”. There is a new invention of the particle’s property, that is: "The particle’s movement can be only deflected at limited and specified angular quantum and that can not be as small as wanted ".