Most of us we know about quantum mechanics. Also I previously done a blog post on the same topic . let's get into to this topic in more advance

Subject I am going to discuss today

1). what is light?

i). wave nature of light
ii). praticle effect of light
iii).Planck expression for energy of light
iv). Einstein expression for energy of light
V). photoelectric effect

2). What is particle ?

i). energy of praticle
ii). position and momentum
iii). inertia
Iv).Dual-Nature of praticle (de-brogley hypothesis)
V).Davison germer experiment
Vi). uncertainty principle
Vii). definition of quantum object

Quantum objects dynamics

1). Schrödinger time dependent one dimensional wave equation

let's get started

On the early days of birth of physics the greatest physicist of all time sir Isaac Newton . Famous for his discovery of universal gravitational force and. Laws of motion. When he started thinking about light. . wait he first started optics . He first invent the reflective telescope or mirror telescope. That is use in Hubble using same principle .
He first suggest that white light consist of 7 colour .. and we all know about his famous disc experiment

When the above disc is in circular motion. It's colour turns out to be white..

Newton 's theory of light

1). according to Newton light is made up of small perfectly elastic praticle he named that corpculus . And know as corpculus theory of light
2).The motion and velocity of small corpculus praticle is different in different medium . because of different in relaxation time.

3).speed of light is Firster in denser medium.

But it's turned out to wrong.

Speed of light is decreases with denser medium. And maximum at vacuum .

So newton idea not accepted.

Thomos young and ralagens phrounhoffer etc theory of light

We all know young for his famous double slit experiment. He suggested that light is a wave He experimental show us that. Light do interference. Polarisation . diffraction . This theory describe almost every nature of light at that time. And Maxwell suggested that light is an electromagnetic wave. Which describe those properties of light .

But it can't describe the black body radiation . photo electric effect. Etc.

Max Planck theory of light

According to max Planck light is consist of quanta .it is discontinues . I.e when he studied black body radiation this assumption holds good and describe the black body radiation at different temperatures perfectly

Energy
E=nhf. Where n=number of quanta
h=Planck constant
f=frequency

The above picture. Visualize the Planck theory of light here the energy is discontinues and also have some definite frequency. They are continues like current it seems to be and discontinues like electron inside the wire. But it's seems to be not true at all because at time of interference it seems to be spread over space. . and it's energy depends upon number of frequency only. As
E=hf

Albert Einstein theory of light

Untill 1900 century no one purely figure out what is light till now light not yet clearly defined . According Einstein special theory of light. Energy and mass are in an equivalent relation .
Impact energy is mass. His famous. Equation. Is known as

E=mc^2

This relation fully proofed both mathematically and experimentally. Who doesn't know about an atomic bombs use the same theory to convert mass into energy. In his general theory of relativity Einstein suggested that light is bended by gravity and amazingly it's turned out true after experimental verification.

For calculating the bending of light in gravity Einstein use his photon theory of light . according to this theory light have dual nature praticle and wave. And energy of a single photon is given by Einstein mass energy relation

E=pc=mc2

Here m=mass of photon
P=momentum
E=energy

Einstein doesn't think about how they are related but he just give a overall idea . How light is a praticle. And this assumption make Einstein GTR possible to calculate how much light bend by gravity.

photoelectric effect

Einstein won Nobel prize for this discovery. When ever light of definite frequency. Is made to fail in an atom mainly in metal electron is ejected from the surface with certain energy. Which only depends upon the frequency of light

Famous equation
T=h(f-ft)
Here T= kinatic energy of electron
h=Planck constant
f=frequency
ft=threshold frequency

This is not described by wave nature of light .
So light have dual nature praticle and wave.

2).What is praticle?

If I say it simply everything in the universe having position and momentum called praticle .

Like ball,chair, planet etc.

i). Praticle have property of inertia
ii). praticle have position while wave spread over space
iii). praticle have energy E=mc2
iv).they interact with other praticle positively while wave do interference .

Dual-Nature of praticle de-brogley hypothesis

I read about de-brogley biography. I found something I want to share something with you
De-brogley claimed that if light have dual nature then praticle must have.

Wavelength=h/mv

When we look at on paper of PhD . It is written that
"I doesn't know how the praticle are wave or light have praticle effect. Because energy some how related to both in same way mc2 for wave and mc2 for praticle. How the same relationship holds good for both . They must have same property. I.e dual object have both wave and praticle nature .

deviation germer experiment

This is the first experiment that proof de-brogley right first evidence come from here that electron exhibits wave like property. Result start of quantum world. .it trigger the Lawes of quantum mechanics . everything gonna right after that discovery Bohr use it to describe the atomic model of hydrogen atoms with great accuracy.

uncertainty principle

Hygenberg proof that a praticle doesn't have both positions and momentum at same instant of time it is a probability function that probably have we can't say there is. an electron we say probably there is an electron. .

Because praticle are waves they must at different place at same time . I.e like on sea there is not a single wave on a point they are all the in sea . If we consider they are praticle wave how do we say exactly where they are . Because they are everywhere wave.

/\x/\p>=h/2pi

This make very difficult to describe the dynamic of system because we can't have exact position and momentum. .

god doesn't play dice Einstein said

After this discovery Schrödinger suggested a probability frame work to describe the quantum object.

His interpretation on this is so simple

It's spread over space just like vector field

And energy must be conserved
Putting this condition.

He discovered

Schrödinger wave equation

The above picture tells us we doesn't have exact position we have bunch of point and darkness represent for probability.