# BEC Help: Annihilation & Creation Operators, S Wave Scattering

• raymo39
In summary, there are several recommended textbooks on Bose-Einstein condensation and related topics such as annihilation and creation operators, s wave scattering, Hamiltonians of dilute BEC's, and the Gross-Pitaevskii equation. These include "Bose-Einstein Condensation in Dilute Gases" by Pethick and Smith, "Bose-Einstein Condensation" by Pitaevskii and Stringari, and "Quantum Liquids" by Leggett. These books use the many-body wavefunction approach rather than the field-theoretical formulation, which some may find more convenient. The Heisenberg picture can also be used to understand these concepts.
raymo39
Hey guys,
im currently doing some stuff on bec's and was wondering if there were any good textbooks out there in general to help be understand annihilation and creation operators, s wave scattering, Hamiltonians of dilute BEC's, Gross-Pitaevskii equation and so forth.

the best books

Pethick and Smith, Bose-Einstein condensation in dilute gases.
https://www.amazon.com/gp/product/052184651X/?tag=pfamazon01-20
Reads like a textbook with exercises to solve after each chapter.

Pitaevskii and Stringari, Bose-Einstein Condensation
http://ukcatalogue.oup.com/product/9780198507192.do
Slightly more technical, also four years older than the above

Leggett, Quantum Liquids
https://www.amazon.com/dp/0198526431/?tag=pfamazon01-20
Leggett's style of presentation is a little quirky, but this one is an expose of the physics of all kinds of BEC and BCS superfluid, with less detail about each. (Not neutron stars, though.) Discusses topics that Leggett thinks are interesting, like coherence.

None of the abovementioned books make use of the field-theoretical formulation, with psi and psi-dagger. That is not necessary in order to study many-body systems (but some think it's more convenient). Instead they go directly for the many-body wavefunction.

Using the many body wavefunction is what I am after, as for QFT, i can pick that up from the basics of the Heisenberg picture and extend what i know there. thank you for this.

## 1. What is a BEC (Bose-Einstein Condensate) and how is it created?

A BEC is a state of matter that occurs at extremely low temperatures. It is created by cooling a gas of bosons (particles with integer spin) to a temperature close to absolute zero, causing them to lose their individual identities and form a single coherent entity.

## 2. What is the significance of annihilation and creation operators in BEC physics?

Annihilation and creation operators are mathematical tools used to describe the behavior of particles in a BEC. They represent the destruction and creation of particles, respectively, and are essential for understanding how particles interact and behave in a BEC.

## 3. How do annihilation and creation operators relate to S wave scattering in BECs?

In BECs, particles interact through collisions that can be described using the concept of scattering. S wave scattering refers to scattering events that occur when particles are approaching each other with zero angular momentum. Annihilation and creation operators are used to describe the behavior of particles during these scattering events.

## 4. Can BEC help with understanding other physical phenomena?

Yes, the principles and mathematical tools used in BEC research have applications in other areas of physics, such as superconductivity and superfluidity. Additionally, studying BECs can provide insights into the behavior of matter at extremely low temperatures.

## 5. How is BEC research being applied in practical applications?

BECs have potential applications in quantum computing, precision measurements, and atom interferometry. They are also being studied as a potential tool for creating new materials with unique properties.

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