# Quantum Mechanics

## Quantum Mechanics Definition:

**Quantum mechanics** or wave mechanics is a branch of mathematical science that helps us understand the wave-like nature of electrons. It is characterized by the wave function (Ψ) developed by Erwin Schrödinger, that relates the location of an electron at a given point in a three-dimensional space to the amplitude of its wave, which corresponds to its energy level.

location or porbability of finding 2. Energy level

## Quantum Mechanics Explained:

To understand quantum mechanics, we must first make up our mind to accept that an electron has both particles as well as wave-like properties. This was the assertion made by scientist Loius De Broglie (de broglie wavelength) which later on dramatically changed the understanding of electrons and laid the foundations for wave mechanics. In the later years, Erwin Schrödinger, Werner Heisenberg (Heisenberg) , and Paul Dirac (Pauli’s exclusion principle) independently incorporated the wavelike nature of electrons in their mathematical models. This new theory is what we call ‘wave mechanics’.

Getting into the mathematics of the wavefunction will be out of the scope of this explanation, but its properties are as follows –

- The wave function (Ψ) is the series of solutions found in the wave equation. The equation describes the total energy of an atom.
- Each wave function corresponds to a specific energy level for an electron. And thus the energy level for an electron is said to be quantized. i.e. an electron can only occupy a discrete energy level.
- The magnitude of the wavefunction at a particular point in space is proportional to the amplitude of the wave at that point.
- The wave function uses three variables to describe the position of an electron.
- The square of the wavefunction at a given point indicates the probability of finding the electron at that point. When we solve for the wave function a large number of times and each time square the value, this leads to a
*distribution of probabilities*in space. Note: this three-dimensional plot of the wavefunction generates an image of an atomic orbital

de broglie wavelength and then the need to understand qhat exactly the wave means

wave particle duality