Paul Dirac proposed a hypothesis called "Large Numbers Hypothesis" (https://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis), where he basically stated that, if he was correct, laws of physics would change with time.
But what about fundamental laws and constants? (Not only 'effective'...
Prominent physicist Paul Dirac proposed a hypothesis that indicated that constants and laws of physics would evolve with time into different constants and laws of nature (https://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis)
This hypothesis was used by Robert Dicke...
Hello,
I remembered once hearing of a must-have quantum mechanics book by Paul Dirac. I don't remember if it was his Principles of QM or Lectures on QM. Based on the table of contents, I believe it was the Principles of QM book; however, looking at both I was thinking about getting his Lectures...
Hi!
I am studying Shankar's "Principles of QM" and the first chapter is all about linear algebra with Dirac's notation and I have reached the section "The Characteristic Equation and the Solution to the Eigenvalue Problem" which says that starting from the eigenvalue problem and equation 1.8.3...
Why does the derivation of the Dirac equation naturally lead to spin ½ particles? The equation is derived from very general starting assumptions, so which of these assumptions has to be wrong to give us a spin-0 or spin-1 particle?
I have tried to search for an answer and got as far as this...
Hello everybody!
I have a doubt in using the chiral projection operators. In principle, it should be ##P_L \psi = \psi_L##.
$$ P_L = \frac{1-\gamma^5}{2} = \frac{1}{2} \begin{pmatrix} \mathbb{I} & -\mathbb{I} \\ -\mathbb{I} & \mathbb{I} \end{pmatrix} $$
If I consider ##\psi = \begin{pmatrix}...
some notes:
There was actually no proof given why ##u^s(p)## or ##v^s(p)## should solve the Dirac equation, only a statement that one could prove it using the identity
$$(\sigma\cdot p)(\bar\sigma\cdot p)=p^2=m^2.$$
We were using the Wely-representation of the ##\gamma##-matrices, if this should...
I was surprised recently to learn that one of the reasons both Newton and Einstein were so revolutionary was that they performed a neat mathematical trick. For Newton, it was the mathematical derivation of Kepler's laws from Newton's laws of gravitation and motion. For Einstein, it was the...
1. Homework Statement
I am studying co- and contra- variant vectors and I found the video at youtube.com/watch?v=8vBfTyBPu-4 very useful. It discusses the slanted coordinate system above where the X, Y axes are at an angle of α. One can get the components of v either by dropping...
In everyday language, beauty is an emotional concept. How would you mix that with quantum physics and the mathematics behind it? Or is what he refers to as "beauty" is more like simplicity? I mean, I agree with the man, the Standard Model feels redundantly complex, but I feel like there is...
Could you, please, give me reference to any paper or talk by Paul Dirac where he expresses his views about or give comments to the de Broglie-Bohm theory (Bohmian mechanics)?
1. Homework Statement
I am trying to fill in the steps between equations in the derivation of the coordinate representation of the Darwin term of the Dirac Hamiltonian in the Hydrogen Fine Structure section in Shankar's Principles of Quantum Mechanics.
$$
H_D=\frac{1}{8 m^2...
In some sources QM is explained using bracket notation. I quite understand algebra of bracket notation, but I do not understand how is this notation related with physically meaningful things? How is bracket notation related to wavefunction notation?
Could you tell me whether following is true...
A system of |1> and |2>, in the beggining has a function |Ψ(0)>= cosa|1> + sina|2>.
The energy of the system is;
https://i.imgur.com/I0C7BFg.png
a, ε,n are known. Find the |Ψ(t)>
The solution is;
https://i.imgur.com/urWs6XW.png
It is known that; |Ψ(t)>= e^(-iHt/ħ) * |Ψ(0)>
but I don't...
1. Homework Statement
\begin{equation}
\int_V (r^2 - \vec{2r} \cdot \vec{r}') \ \delta^3(\vec{r} - \vec{r}') d\tau
\end{equation}
where:
\begin{equation}
\vec{r}' = 3\hat{x} + 2\hat{y} + \hat{z}
\end{equation}
Where d $\tau$ is the volume element, and V is a solid sphere with radius 4...
1. Homework Statement
This isn't a homework problem; it's just something I'm working on and I'm a little confused as to how to go about dealing with what I have. I have several traces of Dirac's gamma matrices, and I know that the trace of an odd number of gamma matrices is zero. So my first...
My professor assigned us to watch the Dirac videos on Youtube:
The video is extremely poor quality. Dirac does speak the equations as he is writing them, so I have been able to catch many of them. I am wondering if a team effort at trying to decipher these would be a worthy effort for all...
Hi,
I'm writing a mathematical expression of energy distribution of a signal, and in the formula I’ve found first and second derivative of delta function. I have to analyze my result but couldn’t found how to read these two derivative from an energy point of view.
And how can we see further...
I am currently reading Modern Electrodynamics by Andrew Zangwill and came across a section listing some delta function identities (Section 1.5.5 page 15 equation 1.122 for those interested), and there is one identity that really confused me. He states:
\begin{align*}
\frac{\partial}{\partial...
I guess my question has multiple parts. Any help in understanding the questions is appreciated.
Assume a single electron in free space. The electron starts moving because of some force applied to it. The source of the force could be pretty much anything, lets say a uniform E-field in X...
Hi everyone. I'm studying for the exam of control theory, and now I'm having an hard time with the response of a system, in particular when we have oscillations.
Suppose you have a system, with a transfer function, say, G(S), in the form:
G(S) = 1
-------------------...
I would like people's opinions on why the negative energy solutions of Dirac's Relativistic Wave equation were simply ignored in 1934 to make things fit. Another related question is with the energy conservation laws as they stand. Why in pair production from a photon at 1.022MeV forming a...
Hey everyone!
It's my first semester with quantum mechanics and I'm uncertain if my solution of this problem is correct, would be nice if someone could check and let me know :smile:
1. Homework Statement
I have to calculate the representation of the state:
|\alpha \rangle \equiv exp[-i...
I have not read any other QM books,i have little knowledge on that subject and want a books that uses mathematics in academic levels but is easy to get the grips on and also builds intuition and explains the phenomenons in a good manner.I do not want a book that emphasizes on mathematics or...
I am still learning about all the Groups related to the Dirac Equation for spin 1/2 particles. Apparently, the reason that the Hilbert Space for spin 1/2 particles is 2-dimensional is because when you try to map SU(2) to SO(3), the mapping is 2-to-1, i.e. SU(2) is a double cover for SO(3)...