Once you are familiar with complex notation you will ask...'why do we use sine and co sine' Feynman lectures in physics are a perfect illustration of the power of complex algebra in physics...look at them if you get the chance.SiuKing666 said:Given that we can satisfy the wave equation with a simple sine & cosine wave function (the real part of the complex wave function) in classical mechanics, why do we use the complex wave function in EM theories?
In QM it is obvious that it gets more mathematically more consistent.
Out of curiosity.
The use of a complex wave function in quantum mechanics is necessary because it is a mathematical representation of a quantum system. It allows us to describe the behavior of particles at the atomic and subatomic level, where classical physics cannot adequately explain their behavior. The complex nature of the wave function accounts for the probabilistic nature of quantum mechanics and allows us to make predictions about the behavior of particles.
A real wave function only takes into account the amplitude of a particle's wave, while a complex wave function also includes the phase of the wave. This phase information is critical in quantum mechanics as it affects the interference patterns of particles and can determine their behavior.
Schrödinger's equation is the fundamental equation of quantum mechanics, and it describes the time evolution of a quantum system. The complex wave function is a solution to this equation and is used to calculate the probability of finding a particle in a particular state at a given time.
No, the complex wave function cannot be visualized in the traditional sense. It represents a mathematical description of a quantum system and has no physical interpretation. However, the square of the wave function, known as the probability density, can be visualized as it represents the likelihood of finding a particle in a particular location.
Yes, complex wave functions have applications in various fields of physics, including electromagnetism, fluid dynamics, and signal processing. They are also used in many engineering and mathematical problems that involve complex numbers and their properties.