# basics of quantum mechanics for dummies

# Basics of Quantum Mechanics for Dummies

Next time when a physics professor says that the probability of your position at any given time, in the whole universe, is never zero, don't think he has lost his marbles. This is where we can start with an explanation of the basics of quantum mechanics for dummies.

*entangled*and choose to behave like waves. According to Niels Bohr, the father of the orthodox '

*Copenhagen Interpretation*' of quantum physics, "

**". Richard Feynman, one of the founders of quantum field theory remarked, "**

*Anyone who is not shocked by quantum theory has not understood it***". Quantum mechanics deals with the study of particles at the atomic and subatomic levels. The term was coined by Max Born in 1924. Though the theory**

*I think I can safely say that nobody understands quantum theory**works*to provide accurate predictions of phenomena at the subatomic scales, there is no real understanding of

*why*it works, what it really

*means*or what implications it has for our world picture. Ergo, the best we can do is present you with the central mystery at the heart of quantum mechanics and show you the way its theoretical structure works to provide real world predictions. Once you decide to go down the rabbit hole, the wonderland of quantum physics, will keep you enthralled forever. So here we go.

*wavefunction*or

*state vector*, that can compute the

*probability*or likelihood of finding a particle. The theory sets fundamental limitations on how accurately we can measure particle parameters, replacing

*classical*determinism with

*probabilistic*determinism. The theory describes just about every phenomena in nature, ranging from the blueness of the sky to the structure of the molecules that make organic life possible.

*any object capable of absorbing radiation at all frequencies and radiating it back*) would emit infinite amount of energy. This was not found to be true experimentally. The energy emitted by a black body seemed to be a function of its frequency, showing a typical bell shaped curve. In 1901, Max Planck came up with an equation that accurately described the energy output of a black body, by introducing the Planck's constant (

**h = 6.626068 x 10**). The Planck relation (

^{-34}m^{2}kg/s**E = hν**

*where E is energy, h is the Planck's constant and ν is the frequency of radiation*), implied that energy could only be traded in '

*packets*' or '

*quanta*'. This discretization brought in by energy quanta was a fundamental shift in thinking, inconsistent with classical institution of physicists at the time. That's why the theory came to be known as

*quantum*physics.

*photoelectric effect*. Classical electromagnetic theory predicted that the number of electrons emitted and their kinetic energy is dependent on the

*intensity*of light reflected from the surface. However, experiments showed that the energy and number of electrons was a function of frequency. Using Planck's energy quantization rule (E = hν ), Albert Einstein conceptualized light as a stream of

*photons*, successfully explaining the photoelectric effect in terms of light frequency. Thus light, which was hitherto known to be a wave, was now known to have a dual character - that of a

*wave and a particle*.

*wave nature*of matter particles.

*Matter Waves*corresponding to every particle, whose wavelength would be inversely proportional to the momentum of the particle.

**λ**(

_{matter}= h / p*where h is the Planck's constant and p is the momentum*)

*wave*nature of particles. The duo fired electrons at a crystallized nickel target to observe wave-like diffraction patterns. Till date, such a pattern was only observed for light waves. Thus it was conclusively proved that particles behave like waves and vice versa. In 1926, Erwin Schrödinger formulated an equation that described the behavior of these matter waves. He successfully derived the energy spectrum of Hydrogen atom, by treating orbital electrons as standing matter waves. Max Born interpreted the square of amplitude of these waves to be the

*probability*of finding associated particles in a localized region. All these developments led to the establishment of quantum mechanics as a scientific theory, well grounded in experiment and formalism. The wavefunction describing any particle in quantum mechanics is a matter wave, whose form is computed through the use of Schrödinger equation. Ergo, matter waves form the central most important feature of quantum mechanics.

**- Werner Heisenberg A direct consequence of the dual (**

*The more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa.**particle/wave*) nature of all matter and energy is the uncertainty principle. In its most non-nerdy version, it states - 'You cannot know the position of a particle and how fast it's moving with arbitrary precision at the same moment.' Or, 'It is fundamentally impossible to simultaneously know the position and momentum of a particle at the same moment with arbitrary accuracy.' Quantitatively, the principle can be stated as follows:

**Δx.Δp ≥ h/2π**(

*where Δx is the uncertainty in position, Δp is the uncertainty in momentum and h is Planck's constant*)

*matter wave*, is inherently delocalized (

*spread out in space*). The more accurately you know the position, more uncertain you are about the momentum and vice versa. Generally, the uncertainty principle is applicable to any dual set of complementary physical quantities that cannot be measured with arbitrary precision.

*fixed*orbit or

*trajectory*goes for a toss. You can no longer plot the path of a particle on a graph, like in Newtonian mechanics. The particle itself being a wave has its position spread out in space. The entirety of information about particles is encoded in the wavefunction Ψ, that is computed in quantum mechanics, using the Schrodinger equation -

*a partial differential equation that can determine the nature and time development of the wavefunction*.

*the wave function*) - for a system, the probability of a particle's position is determined by the square of its modulus - │Ψ│

^{2}.

**So we have**. One unnerving consequence of this fact is that, until a measurement is made, the particle essentially exists in all positions! This paradox was put forward famously in the form of the Schrödinger's cat in the box thought experiment.

*essentially given up on predicting the position of a particle accurately, because of the uncertainty principle. All we can do is predict the probabilities**the cat is both dead and alive*! This is the fundamental paradox presented by the theory. It's one way of illustrating the way quantum mechanics forces us to think. Until the position of a particle is measured, it exists in all positions at the same time, just like the cat is both dead and alive.

*the phenomenon known as quantum entanglement*), frictionless fluid flow in the form of superfluids with zero viscosity and current flow with zero resistance in superconductors. It may one day revolutionize the way computers operate, through quantum computing. It also lays the foundation of advanced theory of relativity, knows as quantum field theory, which underlies all of particle physics.