Dirac Equation: Overview, Questions, Preparation

The Dirac equation was discovered by P.A.M. Dirac n 1928. It is a wave equation and explains the relationship between half-spin electrons and parity inversion. It makes sure that the coordinates of sign inversion of spatial are symmetrical.  The Dirac equation predicates the existence of antiparticles. On the contrary, it also assists the free-moving electrons.

The Dirac equation formula is written as:

(βmc² + c ∑³ n=1 α_n p_n) ψ (x, t) = iℏ  ∂ψ( x , t) /∂t

Here, electron mass is M

The electron wave function is ψ (x, t)

Spacetime coordinates are x, t

Momentum coordinates are p1, p2, p3

Planck constant is ℏ

Speed of light is c

The physical constants show the relation between quantum mechanics and special relativity. Creating the formula was to study the quantum mechanics and special relativity of the electron and manage the atom consistency.

The applications of the Dirac equation are listed below:

1. The Dirac equation is used to solve the paradoxical features of quantum mechanics.
2. In the vacuum, there are a lot of negatively charged electrons that can be studied with the help of 'hole theory'. Dirac equations can resolve it.

Dirac field is used for the substitution of one communication relation into another. In the Dirac field, time equal communications are substituted with time equal anti-communications relations.

1. This equation was formulated in polar form, which states the relation of the derivatives between scalar and pseudoscalar quantities. It can be classified using two degrees of freedom.
2. Dirac equation can be used as a differential equation. Three out of four parts can be constituted as spinor function
3. This equation of Dirac can be constituted with the curved-space time.

Dirac Equation for Class 12

The chapter 'Waves' for class 12 holds a weightage of 5 marks. It includes one very short question of 2 marks and one short question of 3 marks making a total of up to 5 marks.

Example 1. State one application of the Dirac Equation.

Answer: Dirac Equation is used to solve the paradoxical features of quantum mechanics.

Example 2. State the meaning of Dirac.

Answer: Dirac was a physicist who discovered the Dirac equation to know the relationship between half-spin electrons and parity inversion.

Example 3. Write the equation of Dirac using the spin property.

Answer: The equation of Dirac using the spin property is as μD = qS / m.

Q: Who discovered the Dirac Equation?

Q: What is the meaning of Spinor Quantum Mechanics?

Q: What is the formula of the Dirac Equation?

Q: What is a Spinor?

Q: What is the formulation of the Dirac Equation in polar form?