# Dirac Equation vs Wave Function

• B
• bluecap
In summary, the Dirac Equation falls under quantum field theory (QFT), which is the correct explanation for antimatter. Antimatter exists in the Dirac Equation because of the incorporation of complex numbers in QFT, allowing for continuous transformation between states. The use of complex numbers also avoids path cancellation, leading to the Principle of Least Action in the sum over history approach. It is interesting that quantum mechanics is essentially a Wiener process in complex time.

#### bluecap

Hi, under what equation does the Dirac Equation fall under versus that of the Wave Function. Why is Antimatter from Dirac Equation really there but the wave function is not real? Because if Antimatter exist from an equation of complex numbers.. why can't the wave function be real too?

bluecap said:
Hi, under what equation does the Dirac Equation fall under versus that of the Wave Function. Why is Antimatter from Dirac Equation really there but the wave function is not real? Because if Antimatter exist from an equation of complex numbers.. why can't the wave function be real too?

Forget Dirac's equation and holes etc etc. It was simply a beautiful and brilliant way-station to the correct explanation via QFT.

QFT is the correct explanation for antimatter.

Complex numbers are intrinsic to QM. The reason is it allows continuous transformation between states:
http://www.scottaaronson.com/democritus/lec9.html

There are other reasons as well eg you do not get path cancellation so you have the Principle Of Least Action in the sum over history approach without complex numbers. It's interesting, and a bit of a mystery, that QM is basically a Wiener process in complex time.

Thanks
Bill

## 1. What is the difference between the Dirac Equation and the Wave Function?

The Dirac Equation is a mathematical equation that describes how quantum particles, such as electrons, behave. It takes into account both special relativity and quantum mechanics. On the other hand, the Wave Function is a mathematical function that describes the probability of finding a particle in a particular location at a particular time. It is derived from the Schrödinger Equation, which is a non-relativistic version of the Dirac Equation.

## 2. Which one is more accurate - the Dirac Equation or the Wave Function?

Both the Dirac Equation and the Wave Function are accurate in their respective domains. The Dirac Equation is more accurate for particles moving at high speeds, close to the speed of light, while the Wave Function is more accurate for particles moving at slower speeds. Therefore, both equations are important and necessary for understanding the behavior of quantum particles.

## 3. Can the Dirac Equation and the Wave Function be used interchangeably?

No, the Dirac Equation and the Wave Function cannot be used interchangeably. The Dirac Equation is a differential equation that describes the evolution of the wave function over time, while the Wave Function is a mathematical function that represents the state of a particle at a specific time. They are two separate concepts that work together to describe the behavior of quantum particles.

## 4. What are some applications of the Dirac Equation and the Wave Function?

The Dirac Equation and the Wave Function have many applications in theoretical and experimental physics. They are used in fields such as quantum mechanics, particle physics, and condensed matter physics to understand the behavior of particles at the quantum level. They are also used in technologies such as transistors, lasers, and magnetic resonance imaging (MRI).

## 5. Is it possible to solve the Dirac Equation and the Wave Function analytically?

Yes, it is possible to solve the Dirac Equation and the Wave Function analytically for simple systems, such as a single particle in a potential well. However, for more complex systems, numerical methods are often used to approximate the solutions. Additionally, there are many approximate solutions and simplifications of the equations that are used in various applications.