Schrodinger equation in quantum field theory

In summary, QFT looks different from QM because in QFT, the wavefunction is a complete description of the system, whereas in QM, the wavefunction only provides an approximate description.
  • #1
accdd
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What is the Schrodinger equation in QFT? is it the nonrelativistic approximation of a Klein-Gordon scalar field? or Is there more?
I have read that the Schrodinger equation describes a QFT in 0 dimensions.
I accept every answer
 
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  • #2
accdd said:
I have read that the Schrodinger equation describes a QFT in 0 dimensions.
where?
 
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  • #3
accdd said:
What is the Schrodinger equation in QFT? is it the nonrelativistic approximation of a Klein-Gordon scalar field? or Is there more?
I have read that the Schrodinger equation describes a QFT in 0 dimensions.
I accept every answer
It depends. The general Schrodinger equation tells you that time evolution of a quantum state is described by the Hamiltonian. The non-relativistic Hamiltonian gives you then the non-relativistic approximation of whatever field you're considering (spin 1/2, spin 0, ...)
 
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  • #4
@haushofer problem with that is that you are then describing a classical (non-quantum) field.

I can think of the The Schwinger-Dyson equations which in some sense gives the quantum equations of motion.
 
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  • #5
accdd said:
What is the Schrodinger equation in QFT? is it the nonrelativistic approximation of a Klein-Gordon scalar field?
No.

The Schrödinger equation ##i\hbar \dot\psi=H\psi## holds in relativistic quantum field theory for every state ##\psi##, with ##H## being the generator of time translations of the Poincare group.

accdd said:
I have read that the Schrodinger equation describes a QFT in 0 dimensions.
A QFT in 0 space dimensions decribes (in the simplest case) an anharmonic oscillator in the Heisenberg picture, whereas the Schrödinger equation decribes (in the simplest case) an anharmonic oscillator in the Schrödinger picture. Both descriptions are equivalent, but the Schrödinger picture is usually easier to handle, hence is the way most commonly taught.

A nonrelativistic field theory in 3 space dimensions is the second quantized form of the multiparticle Schrödinger equation with an indefinite number of particles.
 
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  • #6
malawi_glenn said:
where?
That sentence is wrong, sorry, I meant to say I read online (a question on stackexchange) that quantum mechanics is related to scalar QFT in 0+1 dimensions. I would like to know more about it.
 
  • #8
Thanks to everyone
 

1. What is the Schrodinger equation in quantum field theory?

The Schrodinger equation in quantum field theory is a mathematical equation that describes the behavior of quantum particles in a field. It is a fundamental equation in quantum mechanics and is used to predict the probability of finding a particle at a certain position and time.

2. How is the Schrodinger equation derived in quantum field theory?

The Schrodinger equation in quantum field theory is derived from the principles of quantum mechanics and special relativity. It combines the concepts of wave functions and operators to describe the behavior of particles in a field.

3. What does the Schrodinger equation tell us about quantum particles?

The Schrodinger equation tells us about the probability of finding a quantum particle at a certain position and time. It also describes how the wave function of a particle changes over time and how it interacts with other particles in the field.

4. How does the Schrodinger equation differ from the classical wave equation?

The Schrodinger equation differs from the classical wave equation in that it takes into account the quantum nature of particles, while the classical wave equation only describes the behavior of classical particles. The Schrodinger equation also includes the concept of probability, which is not present in the classical wave equation.

5. What are the applications of the Schrodinger equation in quantum field theory?

The Schrodinger equation has many applications in quantum field theory, including predicting the behavior of subatomic particles, understanding the properties of materials, and developing new technologies such as quantum computing. It is also used in various fields such as chemistry, biology, and engineering.

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