# Quantum Mechanics

**Introduction: Heisenberg’s uncertainty Principle**

Quantum mechanics is a fundamental branch of physics which generalizes classical mechanics to provide accurate descriptions for many previously unexplained phenomena such as black body radiation, photoelectric eﬀect and Compton eﬀect. The term quantum mechanics was ﬁrst coined by Max Born in 1924.Within the ﬁeld of engineering, quantum mechanics plays an important role. The study of quantum mechanics has lead to many new inventions that include the laser, the diode, the transistor, the electron microscope, and magnetic resonance imaging. Flash memory chips found in USB drives also use quantum ideas to erase their memory cells. The entire science of Nanotechnology is based on the quantum mechanics. Researchers are currently seeking robust methods of directly manipulating quantum states. Eﬀorts are being made to develop quantum cryptography, which will allow guaranteed secure transmission of information. A more distant goal is the development of quantum computers, which are expected to perform certain computational tasks exponentially faster than the regular computers. This chapter attempts to give you an elementary introduction to the topic.

**Explanation:**

We know from the wave-particle duality that every particle has wave-like properties. These wave properties of particles will prevent us from measuring the exact attributes of the particles. This limitation related to the measurements at microscopic level is known as the uncertainty principle. The uncertainty principle states that it is impossible to specify simultaneously the position and momentum of a particle, such as an electron, with precision. The theory further states that a more accurate determination of one quantity will result in a less precise measurement of the other, and that the product of both uncertainties is always greater than or equal to Planck’s constant divided by 4π. That is

This principle was formulated in 1927 by the German physicist Werner Heisenberg. It is also called the indeterminacy principle.

The Heisenberg’s uncertainty principle can also be expressed in terms of the uncertainties involved in the simultaneous measurements of angular displacement & angular momentum and energy & time;

Sometimes h/2π is written as h. In that case the right had side of the uncertainty relations will have h/2.

**Physical significance of uncertainty principles:**

The uncertainty principle is based on the assumption that a moving particle is associated with a wave packet, the extension of which in space accounts for the uncertainty in the position of the particle. The uncertainty in the momentum arises due to the indeterminacy of the wavelength because of the ﬁnite size of the wave packet. Thus, the uncertainty principle is not due to the limited accuracy of measurement but due to the inherent uncertainties in determining the quantities involved. Even though, the uncertainty principle prevents us from knowing the precise position and momentum, we can deﬁne the position where the probability of ﬁnding the particle is maximum and also the most probable momentum of the particle. That means, the uncertainty principle introduces the probabilistic interpretation of the physical quantities. This is the major diﬀerence between the classical physics and quantum mechanics.