[Physics Class Notes] on Quantum Physics Pdf for Exam

The Study of Physics is basically divided into two portions one at the macroscopic level (explained by Newton’s laws of motion or that are at scale of human interaction or experience ) known classical while the behaviour at the microscopic level (that are at the scale of an atom) is studied Quantum Physics.

Need For Quantum Physics

Quantum Physics results in what may appear to be very strange conclusions about the physical world. At the scale of atoms and electrons, many of the equations that we study in classical physics which describe how things move at everyday sizes and speeds, no more appear to be useful. This is because, in quantum physics, objects exist in probability that is they have a certain chance of being at point A, another chance of being at point B and so on as compared  to classical mechanics, where objects exist in a specific place at a specific time.

Dual Behaviour of Matter

Macroscopic objects practically have only particle nature because their wave nature is usually neglected to their large size but on atomic level particles have very less mass and hence both particle and wave nature is considered. This can be termed as dual behaviour as it is displaying both particle and wave nature. The particle nature comes from its mass and the wave nature comes from its matter wave defined by the De-Broglie relationship which is given by,

λ = h/mv

Where,

λ = wavelength of the matter

h = Planck’s constant

m = mass of the matter

v = velocity of matter 

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Laws of Quantum Physics

1) By De Broglie’s equation, we can say that matter also behaves like waves as it relates a moving particle’s wavelength with its momentum. In other words it relates the wavelength associated with a massive particle to its momentum through the Planck’s constant.

De Broglie’s equation says that every moving particle – whether microscopic or macroscopic – is associated with a wavelength.

For microscopic objects, wave nature is observable, but for larger objects, the wavelength is becomes so small as to become unnoticeable

2) Heisenberg’s Uncertainty Principle states that the position and the momentum of a particle cannot be simultaneously measured with arbitrarily high precision. In other words, there is a minimum for the product of the uncertainties of position and momentum.

It is of significance only for microscopic particles because the energy of photons is insufficient to change the position and velocity of larger bodies when it collides with them.

Δx Δp ≥ h /4π

Δx = Uncertainty of state

Δp = Uncertainty of momentum

3) American physicist Arthur Compton highlighted the dual wave and particle nature in his X-ray scattering experiment. He sent a beam of X-rays through a target material and observed that a small part of the beam was deflected at various angles. He also found that the scattered X-rays had longer wavelengths than the original beam. The change in wavelength was explained by assuming that the X-rays scattered from the electrons in the target as if the X-rays were particles with discrete amounts of momentum and energy. When these X-rays are scattered, their momentum is partially transferred to the electrons and recoil electrons take some energy from an X-ray, and as a result the frequency of X-ray is altered. Both the discrete amount of momentum and the frequency shift of the light scattering were completely at variance with classical electromagnetic theory, but they are explained by the Einstein’s quantum formula and the X-rays were assumed to be made up of discrete bundles or particles, now called photons, that lost some of their energy in the collisions with electrons in the target material and it then get scattered at lower energy.

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4) In 1926 the Schrodinger’s wave equation established quantum mechanics in widely applicable form. He postulated that the electrons in an atom should be treated like the waves on the drumhead and the different energy levels of atoms were identified with the simple vibrational modes of the wave equation. Then the wave equation was solved to find these modes, and then the energy of an electron is obtained from the frequency of the mode and from Einstein’s quantum equation, E = hν. Thus, the trajectory, the positioning, and the energy of these systems can be retrieved by solving the Schrödinger’s wave equation. It gives the same energies as Bohr’s original formula but with a much more-precise description of an electron in an atom.