Heisenberg Uncertainty Principle

Introduction of Heisenberg Uncertainty Principle

This prediction of unpredictability is known as Heisenberg uncertainty principle. The uncertainty principle describes the relationship between conjugate variables, like position and momentum or energy and time. In 1927 a German physicist Werner Heisenberg proposed that we cannot measure the position and velocity of an object accurately, simultaneously. This statement however contradicts the existing laws of motion, which clearly has equations for determining both accurately at each instant of time.

Heisenberg’s Equation

We can avoid the confusion if we examine the equation given by Heisenberg. He said that

Where, Δx is the uncertainty in position and Δp is the uncertainty in momentum and h is the Planck’s constant i.e., the product of uncertainty of position and momentum is always greater than a fixed constant.
The above equation can also be written as

Δv is the uncertainty in velocity and m is the mass.

For larger particles, say a man, due to large mass this constant becomes very small and hence the laws of motions gives fairly accurate results.
However for atomic particles the constant has a large value. One can think that these are the uncertainties of the measuring instruments, but actually even if we have a perfect instrument the uncertainty would still exist. This is because of the wave particle dual nature of matter.
To understand this principle we first take a purely sinusoidal wave exhibited by a particle. Since the wave is having a fixed wavelength, using de Broglie’s equation we can precisely tell its momentum as


However, we cannot determine the position of the particle accurately as it is distributed throughout the space in which the wave exists.
Now in another case where we have a combination of various sine waves we obtain a wave with large undulations at certain place compared to rest of the space.

precisely-determined-momentumThe particle is most likely to be found in those places where the undulation of the wave is the greatest. Thus now we do have position with accuracy, but there lies a great inaccuracy in determination of momentum as we cannot ascertain the wavelength of such distorted wave. Thus we see that quite accurate measurement of one quantity leads to huge error in the other.

Heisenberg Uncertainty Principle also true for measuring energy at any instant. This principle states that the exact energy of a particle and exact instant of time at which the energy is possessed by the particle, can not be described with absolute accuracy. If uncertainty of the energy is ΔE and uncertainty of the time is Δt, then

Where, h is same Planck constant.
According to this Heisenberg Uncertainty Principle we cannot predict the exact position of an electron in atom instead we can be able to determine the probability of finding an electron at a particular position. This is done by probability density function which is not in scope of discussion in this article. This function describes electron behavior.

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