Can any one derive Heisenberg principle ?

Question

the formula

Answer 1

Check this out.

Answer 2

Heisenberg also introduced the Uncertainty Principle and this may be written down in two equations: -
Δx. Δp ≈ ħ

And

ΔE. Δt ≈ ħ


The first equation states that the product of the momentum spread (for a quantum entity) and special spread is approximately equal to Planck’s constant divided by 2 pi. In the second equation, the spread of energy and spread of time products are approximately equated to Planck’s constant divided by 2 pi.

In effect the first equations says that, the greater the precision with which we know the value of the position (x), of a quantum entity, then the greater the spread or uncertainty of its momentum and vice a versa. Similarly, from the second equation, the greater the spread in energy, of the quantum particle of entity, then the shorter the time it can exist and again, vice a versa.

A quick partial proof of the first equation may be made as follows. Consider an electron to be a wave packet of allowed wave vectors

k= (2 π/L)(lx,ly,lz)

And an allowed spectrum of frequencies: -

ω = ck = (2 π.c/L) √ (lx,ly,lz)


It may be shown (the actual derivation requires several applications of calculus methods, which are difficult to type down in this answer format) that the special (x) spread of a wave packet as a product of its wave vector spread has the criteria: -

Δx. Δk ≥ 1

Since Δp = ħ Δk a substitution for Δk in terms of Δp gives : -

Δx. Δp ≈ ħ

The second equation may be derived from a consideration and time and frequency spreads (E = hf).

Answer 3

http://en.wikipedia.org/wiki/Uncertainty_principle

Answer 4

for principle

http://en.wikibooks.org/wiki/Quantum_Mechanics/Heisenberg_Uncertainty_Principle

derivation and expalnation
http://en.wikipedia.org/wiki/Uncertainty_principle

Answer 5

I was going to, but.............I'm not there anymore.