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THE LEAST-ACTION PRINCIPLE & QUANTUM MECHANICS. Vu Huy Toan (Vietnam) vuhuytoan@conincomi.vn. 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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THE LEAST-ACTION PRINCIPLE & QUANTUM MECHANICS


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the least action principle quantum mechanics

THE LEAST-ACTION PRINCIPLE & QUANTUM MECHANICS

Vu Huy Toan (Vietnam)

vuhuytoan@conincomi.vn

least action principle and quantum mechanics

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.

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.

V. CONCLUSION.

i introduction
I. INTRODUCTION

Return to the classical mechanics…

the problem is that
The problem is that:
  • According to its definition, function H must be the total energy of the mechanical system gained in the duration of time from t0 to t1. Should we understand this as cause or consequence? Is it actionor effect?
  • What if the action doesn’t reach the least action threshold?
  • What could the mechanical energy state of the micro objects under the action of external force be if this least effect is taken into account?
  • Is the so called “wave-particle dualism” the cause of orbit quantization of electrons in atoms or do they both have other similar causes because they are both associated to Planck constant?
2 least effect and least action
2. Least effect and least action.

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)

iii the least action principle
III. THE LEAST ACTION PRINCIPLE

"For a physical object to change its energy state, the action on it can not be smaller than the least action".

t1-

D =  2E(t)dt  d = h/ (10)

t0-

If E(t) = E = const and  = 1 then:

D = 2E(t1- t0) = 2Et h (11)

this action time interval t can not be too long and must be limited by some conditions
This action time interval ∆t can not be too long and must be limited by some conditions:

- 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

iv consideration of some phenomena on the basis of lap
IV. CONSIDERATION OF SOME PHENOMENA ON THE BASIS OF LAP

1.The movement of PO under the action of a force

  • The action direction of a force coincides with the movement direction of PO
  • Particle moves under the action of perpendicular to movement direction force

2.Wave property of fundamental particles

3. Movementorbit quantization of electron in atom

b particle movement under the action of perpendicular to movement direction force
b) Particle movement under the action of perpendicular to movement direction force

vΔt1

F

α1

A(t0)

B(t1)

Sy= vΔt1sinα1

t0

t2

Figure 5

figure 10 the electron deflection in potential field
Figure 10. The electron deflection in potential field

I2

C

B

A

α3

α2

α1

C’

B’

A’

I1

I0

figure 12 distribution of the double slits potential fields
Figure 12. Distribution of the double slits potential fields

E2(t)+ΔE2 f2(t)+Δf2

e-ΔE E1(t)+ΔE1 f1(t)+Δf1

iv conclution
IV.CONCLUTION

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 ".

slide35
3. In case the movement deflection of an electron in atoms occurs under the action of Coulomb force at uniform angular quantum whose sum is multiplication of 2, the electron’s orbit has a shape of a regular polygon inscribed to a circle with radius rn, from which the orbit quantization condition of electron in atom can be formed.