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Qmechanic ♦
Qmechanic ♦
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numerical Numerical formulation of Dirac equation plus electromagnetic field

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user56771
user56771
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I have the following equations describing the electron field in a (classic) electromagnetic field:

$$ c\left(\alpha _i\right.{\cdot (P - q(A + A_b) + \beta mc) \psi = E \psi } $$

where $A_b$ is the background field and $A$ is the one generated by the local Dirac field

I presume that the equation for the electromagnetic field $A$ generated by the electron would be:

$$\nabla_{\mu}\nabla^{\mu} A_{\nu} = \frac{\psi \gamma^{\nu} \psi}{\epsilon_0} $$

Question: Is there a way to numerically solve these systems of equations to find stable eigenstates of the system?

Side Show Question: Are these eigenstates physically meaningful? do i still need to apply second quantization procedure in order to know which eigenstates are physically meaningful (i.e: stable) and which are not?

I have the following equations describing the electron field in a (classic) electromagnetic field:

$$ c\left(\alpha _i\right.{\cdot (P - q(A + A_b) + \beta mc) \psi = E \psi } $$

where $A_b$ is the background field and $A$ is the one generated by the local Dirac field

I presume that the equation for the electromagnetic field $A$ generated by the electron would be:

$$\nabla_{\mu}\nabla^{\mu} A_{\nu} = \frac{\psi \gamma^{\nu} \psi}{\epsilon_0} $$

Question: Is there a way to numerically solve these systems of equations to find stable eigenstates of the system?

Side Show Question: Are these eigenstates physically meaningful? do i still need to apply second quantization procedure in order to know which eigenstates are physically meaningful and which are not?

I have the following equations describing the electron field in a (classic) electromagnetic field:

$$ c\left(\alpha _i\right.{\cdot (P - q(A + A_b) + \beta mc) \psi = E \psi } $$

where $A_b$ is the background field and $A$ is the one generated by the local Dirac field

I presume that the equation for the electromagnetic field $A$ generated by the electron would be:

$$\nabla_{\mu}\nabla^{\mu} A_{\nu} = \frac{\psi \gamma^{\nu} \psi}{\epsilon_0} $$

Question: Is there a way to numerically solve these systems of equations to find eigenstates of the system?

Side Show Question: Are these eigenstates physically meaningful? do i still need to apply second quantization procedure in order to know which eigenstates are physically meaningful (i.e: stable) and which are not?

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user56771
user56771
  • 873
  • 1
  • 9
  • 16

numerical formulation of Dirac equation plus electromagnetic field

I have the following equations describing the electron field in a (classic) electromagnetic field:

$$ c\left(\alpha _i\right.{\cdot (P - q(A + A_b) + \beta mc) \psi = E \psi } $$

where $A_b$ is the background field and $A$ is the one generated by the local Dirac field

I presume that the equation for the electromagnetic field $A$ generated by the electron would be:

$$\nabla_{\mu}\nabla^{\mu} A_{\nu} = \frac{\psi \gamma^{\nu} \psi}{\epsilon_0} $$

Question: Is there a way to numerically solve these systems of equations to find stable eigenstates of the system?

Side Show Question: Are these eigenstates physically meaningful? do i still need to apply second quantization procedure in order to know which eigenstates are physically meaningful and which are not?