Applications of Complex Analysis in Quantum Physics?

[Tacos]

Hi,

I just finished up a Complex Analysis course last term and, though I'm no physics major, I thought Quantum Physics looked interesting.

Does anyone know some common or interesting applications of Complex Analysis within Quantum Physics? Or even an online resource that might delve into one or two of these applications?

Thanks for any assistance!

 

[malawi_glenn]

Green's functions in scattering theory and propagators:

http://en.wikipedia.org/wiki/Propagator

http://www.oberlin.edu/physics/dstyer/StrangeQM/Klein-Gordon.pdf

One does this to ensure causality.

In quantum field theory, a lot of other integrals comes up where you have to know the tricks of Residue calculus to evaluate them.

Also one has 4-epsilon expansion for the dimensions of the Lagrangian/action, and there one uses analytical continuation.

http://books.google.se/books?id=XYt...X&oi=book_result&resnum=1&ct=result#PPA208,M1

page 208 and forward =)

 

[Mene]

I can definitely attest to the importance and usefulness of Complex Analysis in the field of Quantum Physics. In fact, Complex Analysis is a fundamental tool in understanding and solving many problems in this field. Here are some common and interesting applications of Complex Analysis in Quantum Physics:

1. Wave Functions and Quantum States: In Quantum Mechanics, the wave function is a complex-valued function that describes the state of a quantum system. Complex Analysis is used to analyze and manipulate these wave functions, allowing us to make predictions about the behavior and properties of quantum systems.

2. Quantum Tunneling: This phenomenon, where a particle can pass through a potential barrier even though it does not have enough energy to do so, is a direct result of the complex nature of the wave function. Complex Analysis is used to calculate the probability of tunneling and to understand its implications in various physical systems.

3. Quantum Field Theory: This is a framework used to describe the behavior of particles in terms of fields, which are complex-valued functions. Complex Analysis is used extensively in this field to study the properties and behavior of these fields, and to make predictions about the interactions between particles.

4. Path Integrals: In Quantum Mechanics, the path integral formalism is a powerful tool for calculating the probability amplitudes of quantum systems. Complex Analysis is used to evaluate these integrals and to understand their behavior in different physical scenarios.

5. Quantum Information Theory: This is a rapidly growing field that deals with the processing, transmission, and storage of information in quantum systems. Complex Analysis plays a crucial role in analyzing and manipulating the complex-valued states of these systems, which are essential for quantum information processing.

In addition to these applications, there are many more areas in Quantum Physics where Complex Analysis is used, such as in the study of symmetries, scattering theory, and the behavior of particles in magnetic fields. I would recommend checking out textbooks or online resources specifically focused on the intersection of Complex Analysis and Quantum Physics for a more in-depth understanding of these applications.