# Quantum Mechanics

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### What is Quantum Mechanics?

QM, otherwise known as quantum mechanics, is the branch of physics that deals with the study of the motion of small particles (or quantum particles).

The laws of QM are very different and strange from that of the physical world. At the quantum level, the equation of classical mechanics doesn't work, and the equation of quantum mechanics comes into play. In classical mechanics, things exist at a particular place at a specific time.

However, it doesn't apply to quantum particles. In quantum mechanics, particles exist only in a haze of probability. A particle has a certain chance to be at a point 'A', and also the same probability of being at point 'B.'

The science of quantum mechanics explains the working of the universe with the quantum scale. Quantum mechanics is also called quantum physics or quantum theory.

Mechanics is the study that deals with the motion of objects, and Quantum is a Latin word, which means 'how much'. Quantum energy is the least amount of energy that can exist, and quantum mechanics describes how energy interacts with objects.

### What is Quantum Physics?

Quantum physics is the branch of physics that deals with the study of atomic and subatomic particles. Quantum energy is the minimum amount of energy possible to exist. Quantum mechanics describes how this energy interacts at the subatomic levels.

### What is a Quantum Theory?

Quantum theory is the theoretical science of modern physics. It deals with the study of nature and behavior of matter and energy at the atomic and subatomic levels. The individual unit of the lowest amount of energy is called quanta.

### History of Quantum Mechanics

The history of quantum mechanics began with a number of different scientific discoveries:

• 1838 - Michael Faraday discovered cathode rays.

• 1859–60 - Gustav Kirchhoff has the winter statement of the black-body radiation.

• 1877 - Ludwig Boltzmann suggested that the energy states of physical systems can be discrete in nature.

• 1887 - Heinrich Hertz discovered the photoelectric effect.

• 1900 - Max Planck gave the quantum hypothesis according to which the energy-radiating subatomic systems can be made a division of a number of discrete 'energy elements' ε.

It also states that these energy elements are proportional to the frequency of the radiated energy. It is given by the formula:

∈ =hv

Where h = Planck's constant.

### Quantum Mechanics Formulas

Quantum mechanics is defined through formulation in terms of operators, probabilities, matrices, momentum, wavelength quantities, and in terms of energy.

For the properties encountered on a macroscopic scale-like force, there is little or no treatment.

1. Wave-Particle Duality

Massless Particles, Photons

Planck–Einstein Equation, E = hf = $\frac{hc}{λ}$

Photon Momentum p =  $\frac{hf}{c}$  = $\frac{h}{λ}$

1. Massive Particles

De Broglie Wavelength gth, p= $\frac{h}{λ}$ = h-k

Heisenberg’s Uncertainty Principle = xp ≥  $\frac{h-}{2}$

Et ≥ $\frac{h-}{2}$

Some typical effects which only Quantum theory can explain, and in part, are the cause for the rise of Quantum mechanics itself, are the following.

1. Photoelectric Effect

Photons greater than threshold frequency incident on a metal surface causes (photo) electrons to be emitted from the surface

Ek max = hf = ф

1. Compton Effect

Change in wavelength of a photon from an X-ray source depends only on the scattering angle

Δλ=  $\frac{h}{2m}$ (1-cosθ)

1. Moseley's Law

The frequency of the most intense X-Ray Spectrum (K-α) line for an element, Atomic Number Z

f =  $\frac{c}{λ}$  = MK(Z-1)2

MK = 2.47 X1015 Hz

I is spectral radiance (Wm‾2 sr-1 Hz-1 for frequency or W m-3 sr-1 for wavelength) not simply intensity (W m-2)

l(v,T) = $\frac{2hv^{3}}{c^{2}}$ $\frac{1}{e_{kt}^{hv}-1}$

l($\lambda$,T) =$\frac{2hc^{2}}{\lambda^{5}}$ $\frac{1}{e_{\lambda kt}^{hv}-1}$

### What is the Quantum Mechanical Model?

There are two models of atomic structure that are in use today; they are the Bohr model and the quantum mechanical model. The quantum mechanical model is totally based on mathematics and is used to explain the functions of complex atoms.

The quantum mechanical model is based on quantum theory. According to quantum theory, matter exhibits properties of waves also, and it is not possible for finding the exact momentum and position of a quantum particle at the same time. This principle is called the Uncertainty Principle.

Some of the Proposed Ideas for the Quantum Mechanical Model are:

●Louis de Broglie proposed that all types of matter have some particles matter waves and hence a wavelength λ, which is given by the following equation:

λ = h​/mv

●The quantum mechanical model of an atom was proposed by Erwin Schrödinger, according to which electrons have some matter waves.

●As per the Heisenberg uncertainty, the more we know about the position of an electron, the less we know about its energy and vice versa.

●Electrons have an intrinsic property called spin, which can either be one of two possible values of spin: spin-up or spin-down.

●If two electrons occupy the same orbital in an atom, then they must have opposite spins.

1. What are the Uses of Quantum Mechanics?

Ans- Here are some of the uses of quantum mechanics:

● It helps us to understand the properties of molecules and atoms in a better way.

● It helps to understand the working principle of stars, galaxies, and the entire universe.

● Quantum mechanics forms the basis of the theory of Big Bang, which states how the universe began.

Every matter attracts every other matter because of gravitational force. Einstein explained it in his theory of general relativity.

However, some conclusions of quantum mechanics do agree with that theory. It is because of quantum mechanics that some technologies like:

• Spectroscopy,

• MRIs,

• Lasers,

• CDs and DVDs

2. What are the 4 Quantum Mechanics?

Ans- The four sectors of quantum mechanics are:

1. Quantization of physical properties

2. Quantum entanglement

3. Uncertainty principle

4. Wave-particle duality

3. What Exactly is Quantum?

Ans- Quantum (plural quanta) is the minimum possible amount of any physical entity. Quantization of energy and its influence on the interaction of energy and matter (quantum electrodynamics) is a part of the fundamental framework. This helps us to understand and describe the properties of nature.

4. What is the difference between the Quantum Model & the Bohr Model?

Ans- In the Bohr Model, the electron is treated as a particle that orbits in its fixed orbit around the nucleus.

In the Quantum Mechanical Model, the electron is considered as a wave.