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Quantum Mechanics-

Introduction-

The reason behind the establishment of Quantum Mechanics was the failure of classical mechanics, classical mechanics was unable to answer the reason behind the observed Spectrum of Black body radiation. The new formed mechanics was named as Quantum Mechanics behind the word Quanta means the discrete packet of energy (quantum of EM field is known as Photon) or simply discrete quantity.

The reason found behind by the spectrum was that the electromagnetic energy is not emitted continuously but is emitted in form of discrete value i.e. Quantum.

Quantum Theory-

It is a Modern physics theory that discusses the nature and behavior of matter and energy on atomic and sub-atomic levels. It was initialized by the well known physicist also known as father of Quantum Physics - Max Planck. In 1900 he discovered the reason behind the change of color of a hot body, i.e. when a body is heated it changes from Red to Orange to Blue as its temperature is increased. He assumed that energy exist in discrete individual units similar to matter not just a constant EM wave.
He observed that at discrete temperature level energy from a glowing body occupy different areas of color spectrum. Planck wrote a mathematical expression {E = nnh} to show these individual units of energy (Quanta) here 'h' is Planck constant having a value =6.625x10-34 Joule-sec,n stands for the oscillating frequency of particle and n is an integer. So comes that the energy flow in form of discrete packet each having a value of 'hn'. He also gave a Planck's Radiation formula which was mathematically proving the spectrum of Black Body Radiation.  This was the start of quantum physics.

Quantum Physics Overview, Concepts and History-

After the theory from Planck many scientists start their work in the field of Quantum Physics and the well know of them along with their work includes Albert Einstein, in 1905 he stated that not only energy (as said by Planck) but even the radiation was Quantized too. He proved the Photoelectric Effect i.e. the dual nature of light was first time screened i.e. the absorption of photon from light causes the release of electrons only if the falling frequency of Photon is greater than the threshold frequency or the wavelength is smaller than the threshold wavelength, note-Electron emission is independent of intensity but the amount of emission is proportional to the Intensity of photon. In 1916 he explained the spectrum of black body radiation denoted by Max Planck by the interaction of photons with new Bohr's atoms.

Another Effect popular in culture is Compton effect this also shows the dual nature of light, It was accidentally performed by a Physicist Compton, while a X-ray was scattered from a thin metal sheet he observed that the wave length was shifted, this shift in wave length was not explainable by the classical mechanics cause there must have been no energy loss while a wave collision, in the Quantum theory it was explained as that due to the absorption of a part of energy by the electron in metal sheet the energy of photon decreases and hence acting as a particle the photon loses its energy and causes a shift  in wavelength denoted by  Δλ, were λ is initial wavelength and λo is the final wavelength

so after setting and solving change of momentum equation for photon and electron we can finally obtain Δλ= λo- λ =h(1-cos?)/mc, here ? is the angle with which the photon deviate after the collision, m is mass of electron and c is velocity of light. It was notated that the Δλ was independent of λo and its intensity is directly proportional to the Frequency, n.

Next scientist to be included is Louis de Broglie, in 1924 he propose that there is no fundamental difference between the makeup and behavior of matter and energy i.e. on atomic and sub-atomic level both of them can behave as particle or as a wave and hence this theory was coined as 'wave-particle duality'. He deduced that the wavelength (λ) is inversely proportional to particle's momentum (p) and this wavelength is also called de-Broglie wavelength. Einstein derived E=pc in his theory of special relativity , 'E' for energy 'p' for momentum and 'c' for speed of light and as we know E = nh and c/λ = n, we can conclude  {λ=h/p}, λ is the de-Broglie wavelength for Electromagnetic waves as well as for Matter.

This theory was experimentally proved by Davison and Germer three years later and experiment was known as Davison-Germer experiment-

It consist of a electron gun made up of heated filament which shoots electron, electrons where released due to the thermal excitement but the acceleration was due to the potential difference. On the opposite end was a nickel crystal and the detector moves along an arc recording the scattering, whole experimental setup was vacuumed.

The closer to the 1900-1930 was given by Werner Heisenberg, in year 1927 he said that knowing precise, simultaneous measurement of two complementary values such as momentum and position of a sub atomic particle is technically impossible. According to him the more precision we try to give on one value makes the precision of other value get duller. This theory is known as the Heisenberg uncertainty principle, and hence on this Albert Einstein commented "God does not play dice".

Some other important topics-

Schrödinger Wave Equation- After years of discussion Schrodinger was the first person able to write a wave equation in actuality. His equation was a fundamental equation of physics for describing the Quantum Mechanical behavior; it is partial differential equations that describe how the wave function evolve over time, his equation is in two form time dependent and time independent, and in 1-D and 3-D form.

This wave functions physical interpretation is that it enables us to know the probability of finding a particle at a certain point in space.

Six Things about Quantum Physics every student shall know-

1) Everything, even particles are made of waves -
As discussed above we know about the dual-nature of matter shown by de-Broglie who even gave a mathematical relation between the wave and particle nature of matter as well as for energy, for a example the light is a form of energy which enable us to see is made up of small energy packet known as photon and is having wave nature as shown in Photo Electric effect & also in Compton effect.

2) Quantum physics is not continuous but discrete -
As given in the Quantum theory by Max Planck, the electromagnetic energy is emitted in form of discrete energy packets with each packet having the energy 'nh Joules', and Albert Einstein quoted that not only energy but even matter is discrete.

3) Quantum physics is not predicable but is Probabilistic -
As told by Heisenberg that it is not possible to know the momentum as well as the position of a election precise and simultaneously and hence the Schrödinger Wave Equation come in play to let us know the probability of the particle at a given position in space

4) Quantum Mechanics is very Small -
Quantum Physics is weird as the effect goes smaller as soon as the object gets larger i.e. as the wave nature dominates the particle nature diminishes and vice versa so to follow wave nature or to go for Quantum study we need object to be at speed comparable to light or require it to be very small.

5) Quantum Mechanics is not-local -
In 1935 Albert Einstein with his fellows published a mathematical equation also known as EPR which state that Quantum physics is actually non-local i.e. measurements measured at microscopic stage is not only influenced by its immediate surroundings but is influenced by non-local elements too.

6) Quantum Physics or mechanics is not Magic-
How weird or abrupt it may seem, but yet Quantum Physics is not at all a magic, nor is a work of God. There is a reason and technical correct answer behind every dramatic turn of Quantum physics and the turns which are not yet resolved will be resolve in future.

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