Tagged Questions
6
votes
3answers
211 views
Why is the Dirac equation not used for calculations?
From what I understand the Dirac equation is supposed to be an improvement on the Schrödinger equation in that it is consistent with relativity theory. Yet all methods I have encountered for doing ...
2
votes
0answers
61 views
Relativistic genarization of Quantum Harmonic Oscillator
I am trying to find out relativistic description of a quantum harmonic oscillator.
For a classical relativistic oscillator mass is a function of co-ordinates(http://arxiv.org/abs/1209.2876).
...
9
votes
1answer
296 views
Dimension of Dirac $\gamma$ matrices
While studying the Dirac equation, I came across this enigmatic passage on p. 551 in From Classical to Quantum Mechanics by G. Esposito, G. Marmo, G. Sudarshan regarding the $\gamma$ matrices:
...
1
vote
0answers
159 views
Matrix manipulation for Dirac matrices
From the Dirac equation in gamma matrices, we know that $$\gamma^i=\begin{pmatrix}
0 & \sigma^i \\
-\sigma^i & 0
\end{pmatrix}$$ and $$\gamma^0=\begin{pmatrix}
I & 0 \\
0 & -I
...
3
votes
2answers
199 views
Matrix operation in dirac matrices
If we define $\alpha_i$ and $\beta$ as Dirac matrices which satisfy all of the conditions of spin 1/2 particles , p defines the momentum of the particle, then how can we get the matrix form ?
...
4
votes
1answer
453 views
What is the relativistic particle in a box?
I know people try to solve Dirac equation in a box. Some claim it cannot be done. Some claim that they had found the solution, I have seen three and they are all different and bizarre. But my main ...
1
vote
2answers
99 views
3
votes
1answer
195 views
Energy spectrum of a Dirac electron
How do you explain easily "The spectrum of an electron in a repulsive potential " and hence "bound state of charge conjugation" in Dirac hole theory ?
0
votes
1answer
417 views
Charge conjugation in Dirac equation
I need to know the mathematical argument that how the relation is true $(C^{-1})^T\gamma ^ \mu C^T = - \gamma ^{\mu T} $ .
Where $C$ is defined by $U=C \gamma^0$ ; $U$= non singular matrix , $T$= ...
2
votes
4answers
478 views
Why would Klein-Gordon describe spin-0 scalar field while Dirac describe spin-1/2?
The derivation of both Klein-Gordon equation and Dirac equation is due the need of quantum mechanics (or to say more correctly, quantum field theory) to adhere to special relativity. However, excpet ...
0
votes
1answer
349 views
Solution to Klein-Gordon equation always valid?
We know that there is a relativistic version of Schrodinger equation called Klein-Gordon equation. However, it has some problems and due to these problems, there is Dirac equation that handles these ...
1
vote
1answer
162 views
Complete set and Klein-Gordon equation
In http://www.physics.ucdavis.edu/~cheng/teaching/230A-s07/rqm2_rev.pdf, it says that when there is some external potential, the Klein-Gordon equation is altered, and it says the following:
The ...
2
votes
1answer
221 views
Explanation of equation that shows a failed approach to relativize Schrodinger equation
I'm reading the Wikipedia page for the Dirac equation:
$\rho=\phi^*\phi\,$
......
$J = -\frac{i\hbar}{2m}(\phi^*\nabla\phi - \phi\nabla\phi^*)$
with the conservation of probability ...
0
votes
1answer
216 views
How did one get the defining equation of probability current and conservation of probability current and density?
I'm reading the Wikipedia page for the Dirac equation:
$$\rho=\phi^*\phi$$
and this density is convected according to the probability current
vector
$$J = ...
1
vote
1answer
227 views
How to obtain Dirac equation from Schrodinger equation and special relativity?
I'm reading the Wikipedia page for the Dirac equation:
The Dirac equation is superficially similar to the Schrödinger
equation for a free massive particle:
A) ...
2
votes
1answer
246 views
How to construct the charge conjugation matrix for any given dimension?
Generally, Gamma matrices could be constructed based on the Clifford algebra.
\begin{equation}
\gamma^{i}\gamma^{j}+\gamma^{j}\gamma^{i}=2h^{ij},
\end{equation}
My question is how to generally ...
2
votes
1answer
212 views
Magnetic moment derivation from Dirac equation
I am reading a text book where they show the electron has spin 1/2 using Dirac's equation. At one point in the derivation they define $\pi=P-qA/c$ where $P$ is the momentum operator and A is the ...
0
votes
0answers
59 views
Is it necessary to use all solutions when calculating an expectation value in a spin state?
I'm given an spinor $\Psi$ which is solution of the Free Dirac equation, such that is an eigenfunction of $\hat{\vec{p}}$ and has positive energy. Then I'm asked to calculate the expectation value of ...
1
vote
2answers
327 views
Spin matrices in Dirac equation
Why in every textbook when deriving Dirac's equation the smallest possible matrices ($2 \times 2$) are used?
I wonder why one couldn't use spin 1 matrices ($3 \times 3$) and get relativistic equation ...
3
votes
4answers
675 views
Where is spin in the Schroedinger equation of an electron in the hydrogen atom?
In my current quantum mechanics, course, we have derived in full (I believe?) the wave equations for the time-independent stationary states of the hydrogen atom.
We are told that the Pauli Exclusion ...
5
votes
4answers
785 views
Why are four-vectors needed in the Dirac equation, when there are 4 linearly independent 2D matrices?
I was taught that for the Dirac-equation to "work", you need matrices of the following form:
$Tr(\alpha^i) = 0$.
Eigenvalues +1 or -1
2 previous points together: equal number of negative and ...
7
votes
4answers
681 views
Dirac equation on general geometries?
I have a numerical method for computing solutions to the Dirac equation for a spin 1/2 particle constrained to an arbitrary surface and am interested in finding applications where the configuration ...
5
votes
7answers
762 views
Evolution in the interpretation of the Dirac equation
As I understand, Dirac equation was first interpreted as a wave equation following the ideas of non relativistic quantum mechanics, but this lead to different problems.
The equation was then ...
