Dirac Definition and 900 Threads

Paul Adrien Maurice Dirac (; 8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century.Dirac made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics. Among other discoveries, he formulated the Dirac equation which describes the behaviour of fermions and predicted the existence of antimatter. Dirac shared the 1933 Nobel Prize in Physics with Erwin Schrödinger "for the discovery of new productive forms of atomic theory". He also made significant contributions to the reconciliation of general relativity with quantum mechanics.
Dirac was regarded by his friends and colleagues as unusual in character. In a 1926 letter to Paul Ehrenfest, Albert Einstein wrote of Dirac, "I have trouble with Dirac. This balancing on the dizzying path between genius and madness is awful." In another letter he wrote, "I don't understand Dirac at all (Compton effect)."He was the Lucasian Professor of Mathematics at the University of Cambridge, was a member of the Center for Theoretical Studies, University of Miami, and spent the last decade of his life at Florida State University.

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  1. F

    Dirac Delta Function Help: Justifying Translation/Sifting Property

    I have been reviewing some details on the Dirac Delta function and I've hit a little bit of a road block with trying to wrap my head around how the Translation/Sifting property of the function is justified. Now according to my text the overall definition is the generalized function with the...
  2. H

    Dirac Expression for Vector Potential of a Magnetic Monopole Problem

    Hi, Homework Statement Consider the vector potential, \vec{A}(\vec{x}), below. The problem is to calculate \vec{A}(\vec{x}) explictly, and show that it has components A_{r}, A_{\theta} and A_{\phi} Homework Equations \vec{A}(\vec{x}) = \frac{g}{4\pi} \int_{-\infty}^{0} \frac{dz'...
  3. N

    Dirac Notation and Hermitian operators

    Homework Statement Using Dirac Notation prove for the Hermitian operator B acting on a state vector |ψ>, which represents a bound particle in a 1-d potential well - that the expectation value is <C^2> = <Cψ|Cψ>. Include each step in your reasoning. Finally use the result to show the...
  4. C

    [Srednicki] Charge Conjugation of Dirac Spinor

    Homework Statement I am reading Srednicki's QFT up to CPT symmetries of Spinors In eq. 40.42 of http://web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf I attempted to get the 2nd equation: C^{-1}\bar{\Psi}C=\Psi^{T}C from the first one: C^{-1}\Psi C=\bar{\Psi}^{T}C Homework Equations...
  5. E

    Properties of the Dirac point and Topological Insulators

    I understand that the centring of the Fermi energy at the Dirac point is a highly sought after property in Topological Insulators but I'm unsure as to exactly why? I see that the state at the conical intercept will be unique but I'm not sure of what is theorized to happen to the electrons...
  6. L

    Inner product of dirac delta function

    Homework Statement Find the inner product of f(x) = σ(x-x0) and g(x) = cos(x) Homework Equations ∫f(x)*g(x)dx Limits of integration are -∞ to ∞ The Attempt at a Solution First of all, what is the complex conjugate of σ(x-x0)? Is it just σ(x-x0)? And I'm not sure how to...
  7. R

    Does the Dirac ground state of the H atom have an electron current?

    I have confounded myself with the following observation. Take the standard expression for the lowest energy Dirac 4-spinor solution of the Dirac equation with a Coulomb potential (the H atom ground state). Plug this into the standard expression for the 4-vector current and use values for the...
  8. W

    Integral of Dirac times Heaviside

    I am trying to solve the integral \int_{-\infty}^\infty H(x) \delta(x) dx Where H(x) is a unit step and d(x) is a standard Dirac delta. Mathematica chokes on this, but I'm pretty sure that the value is \int_{-\infty}^\infty H(x) \delta(x) dx = \dfrac12 \left(H(0^+) + H(0^-) \right) =...
  9. P

    Eigenfunctions and dirac notation for a quantum mechanical system.

    QUESTION A quantum mechanical system has a complete orthonormal set of energy eigenfunctions, |n> with associate eigenvalues, En. The operator \widehat{A} corresponds to an observable such that Aˆ|1> = |2> Aˆ|2> = |1> Aˆ|n> = |0>, n ≥ 3 where |0> is the null ket. Find a complete...
  10. R

    Solving the time dependant schrodinger eqn in dirac (bra ket) notation

    given: at t=0 |PSI(0)> = 1/2 |PSI1> + (SQRT3)/2 |PSI2> --------------------------------------------------------------------- my attempt so far: we can write |PSI1> = 1/2 |UP> + 1/2 |DOWN> |PSI2> = (SQRT3)/2 |UP> + (SQRT3)/2 |DOWN> therefore |PSI(0)> = 1/2 |UP> + 1/2...
  11. N

    Simplifying equations involving Dirac Delta (Analog Signal Processing)

    Homework Statement I'm specifically having trouble with taking the Fourier transform of f(t) in order to sketch F(w) and also to move on with the rest of the problem. Homework Equations f(t) = (5+rect(t/4))cos(60pi*t) mixed_signal = cos(60pi*t) The Attempt at a Solution I attempted to...
  12. A

    Proof that a Dirac particle has spin 1/2?

    Hi, I am having trouble following the Peskin and Schroeder and their derivations to show that a Dirac particle is a spin 1/2 particle (page 60 and 61). I understand how he gets the first (unnumbered) equation on page 61. However, I don't understand how he gets to the second equation...
  13. A

    Relation between residue integration and the Dirac Delta function

    Homework Statement OK so I'm doing a course on Signals and Systems and I'm taking inverse z transforms using residue integration. One particular formula in complex integration made me think a bit. \oint{\frac{f(z)}{z-z_0} dz} = 2\pi jf(z_0) This looks eerily similar to the definition...
  14. L

    Dirac Delta Integrals: How to Solve for the Argument of the Delta Function?

    Homework Statement This is just an example, not a specific problem. So if I have ∫σ(sinx), for example, and my limits of integration are, for example, 1 to 10, what I need to do to solve that is to find a value of x that would make the argument of the delta function 0. So for sinx, 0 makes...
  15. M

    How to Derive the Time Evolution of Expectation Values in Quantum Mechanics?

    Hi everyone, my problem is this Using Dirac notation show that \frac{d}{dt}<\varphi|\hat{A}|\varphi> = \frac{i}{\hbar}<\varphi|[\hat{H},\hat{A}]|\varphi> where A does not explicitly depend on t I am given as a hint that the hamiltonian operator in Dirac notation is...
  16. A

    Dirac Delta function and Divergence

    Homework Statement The Potential V(r) is given: A*e^(-lambda*r)/r, A and lambda are constants From this potential, I have to calculate: E(r), Rho(r) -- charge density, and Q -- total charge. Homework Equations The Attempt at a Solution I know that E(r) is simply minus...
  17. U

    What is a Dirac delta and how is it used as a functional in linear operators?

    What is the sum of an infinite Dirac series and why? 1 or infinity? \sum_{n=-\infty}^{\infty}\delta (n) I can see it being 1 because it's like a series version of the integral: \int_{-\infty}^{\infty}\delta (t)dt = 1 But for the series where n=0, \delta (0) = \infty :confused:
  18. P

    Understanding Dirac Notation in Quantum Mechanics

    1.) an inner product of a state vector represent by <\psi|\psi>. sometimes the notation is like <\phi|\psi> is mean transfer from state |\psi> to <\phi|.it mean the former 1 do not transfer the state? what is the difference between both? 2.) what is mean by <x|\psi>? is it mean x(position)...
  19. skate_nerd

    Proving a property of the dirac delta function

    Homework Statement Prove this theorem regarding a property of the Dirac Delta Function: $$\int_{-\infty}^{\infty}f(x)\delta'(x-a)dx=-f'(a)$$ (by using integration by parts) Homework Equations We know that δ(x) can be defined as...
  20. F

    Residue of Dirac delta function?

    Does the Dirac delta have a residue? It seems like it might, but I don't know how to attack it, since I really know very little about distributions. For example, the Dirac delta does not have a Laurent-expansion, so how would you define its residue?
  21. S

    Why Doesn't the Fourier Series of a Dirac Comb Match Pointwise Values?

    http://en.wikipedia.org/wiki/Dirac_comb Please have a look at the Fourier Series section, and its last equation. Let T = 1. After expanding the Equation x(t) = 1 + 2cos(2∏t) + 2cos(4∏t) + 2cos(6∏t) ... Now this does not give the original Dirac Comb. Eg: at t = 1/2 x(1/2) = 0 But RHS =...
  22. M

    How Does Dirac Delta Substitution Relate to Helmholtz's Decomposition Theorem?

    Hi All, I found (Wikipedia page on Helmotz's decomposition theorem) the follwoing equality, which puzzles me: $$\delta(x-y) = - (4 \pi)^{-1} \nabla^{2} \frac{1}{\vert x - y \vert}$$ I am not sure I understand, the r.h.s seems to me a proper function. The page mentions this a sa position...
  23. Philosophaie

    Dirac Delta Function: What It Does & How to Evaluate It

    What does the Dirac Delta Function do? ##\delta^3(\vec{r})## How do you evaluate it? What are its values from -inf to +inf?
  24. snoopies622

    Interpreting the Dirac equation

    Why does the \psi of the Dirac equation return four complex numbers instead of one, as in the Schrodinger equation? I know it has something to do with spin, but I'm not finding a clear answer to this question in my sources. What do these four complex numbers represent?
  25. Vahsek

    Dirac Delta Function: Definition & Mathematics

    It's been quite some time now since I decided to stop self-studying physics and to pay more attention to the math behind. I'm working towards gaining an understanding of 100% rigorous mathematics for now. One thing that has always bothered me is the Dirac delta function. What I want to know...
  26. J

    Source of Dirac Field: Classical & Quantum Explanation

    Classically as well as quantum-mechanically, the source of the Maxwell field is the electron/four-current (Dirac field), so the use of the Green Function propagator for the Maxwell field makes perfect sense: the Maxwell field is inhomogenous in the presence of matter. But what about the source...
  27. P

    Is δ(x+y)=δ(x-y) for Dirac Delta Function?

    Homework Statement Good day. May I know, for Dirac Delta Function, Is δ(x+y)=δ(x-y)? The Attempt at a Solution Since δ(x)=δ(-x), I would say δ(x+y)=δ(x-y). Am I correct?
  28. S

    The nature of the dirac delta function

    From what I can tell, it seems that 1/x + δ(x) = 1/x because if we think of both 1/x and the dirac delta function as the following peicewise functions: 1/x = 1/x for x < 0 1/x = undefined for x = 0 1/x = 1/x for x > 0 δ(x) = 0 for x < 0 δ(x) = undefined for x = 0 δ(x) = 0 for x > 0...
  29. D

    Partial differential equation-delta Dirac& Heaviside function

    I got 2 questions to ask! I have finished one but not sure if it's correct so I need to double check with someone :) http://imageshack.us/a/img708/1324/83u8.png Here is my worked solution, I took this picture with my S4 and I wrote is very neatly as I could! The reason I didn't type it all...
  30. P

    The Double Dirac Delta Function Potential wave functions

    Homework Statement Consider the double Dirac delta function V(x) = -α(δ(x+a) + δ(x-a)). Using this potential, find the (normalized) wave functions, sketch them, and determine the # of bound states. Homework Equations Time-Independent Schrodinger's Equation: Eψ = (-h^2)/2m (∂^2/∂x^2)ψ +...
  31. P

    A question about Dirac Delta Potential Well solution

    In Griffith's Introduction to Quantum Mechanics, on page 56, he says that for scattering states (E > 0), the general solution for the Dirac delta potential function V(x) = -aδ(x) (once plugged into the Schrodinger Equation), is the following: ψ(x) = Ae^(ikx) + Be^(-ikx), where k = (√2mE)/h...
  32. Y

    Question about Dirac Delta function

    In page 555, Appendix B of Intro to electrodynamics by D Griffiths: \nabla\cdot \vec F=-\nabla^2U=-\frac{1}{4\pi}\int D\nabla^2\left(\frac{1}{\vec{\vartheta}}\right)d\tau'=\int D(\vec r')\delta^3(\vec r-\vec r')d\tau'=D(\vec r) where ##\;\vec{\vartheta}=\vec r-\vec r'##. Is it supposed to be...
  33. Y

    How Do I Prove Symmetry and Scaling Properties of the Dirac Delta Function?

    I want to proof (1)##\delta(x)=\delta(-x)## and (2) ## \delta(kx)=\frac{1}{|k|}\delta(x)## (1) let ##u=-x\Rightarrow\;du=-dx## \int_{-\infty}^{\infty}f(x)\delta(x)dx=(0) but \int_{-\infty}^{\infty}f(x)\delta(-x)dx=-\int_{-\infty}^{\infty}f(-u)\delta(u)du=-f(0) I cannot proof (1) is equal as I...
  34. Y

    Question on Dirac Delta function in Griffiths

    My question is in Griffiths Introduction to Electrodynamics 3rd edition p48. It said Two expressions involving delta function ( say ##D_1(x)\; and \;D_2(x)##) are considered equal if: \int_{-\infty}^{\infty}f(x)D_1(x)dx=\int_{-\infty}^{\infty}f(x)D_2(x)dx\;6 for all( ordinary) functions f(x)...
  35. snoopies622

    Potential energy in the Dirac equation

    Why does the Dirac equation not have a potential energy term? The Schrödinger equation does, and the Dirac equation is supposed to be the special relativity version of the Schrödinger equation, no?
  36. D

    Dirac Delta Function: Explanation & Usage

    I know this probably belongs in one of the math sections, but I did not quite know where to put it, so I put it in here since I am studying Electrodynamics from Griffiths, and in the first chapter he talks about Dirac Delta function. From what I've gathered, Dirac Delta function is 0 for...
  37. P

    Dirac trace in D dimension with gamma_5

    I know the trace tr[\gamma_5 a\!\!\!/b\!\!\!/c\!\!\!/d\!\!\!/] in 4-dimensional space-time, how is the result of it in D dimension? Is it the same as in 4 dimension?
  38. N

    A question about Dirac equation.

    It seems that notions of quantum field and wave function are utterly different from each other.Then is Dirac equation being equation for field or for relativistic wave function or for the both?
  39. L

    Undergraduate-level explanation of Dirac Equation?

    I am interested in learning about how the Dirac Equation was derived, how it allowed special relativity and QM to be unified, and how it predicted the existence of animatter. The explanations I have found so far are too advanced for me mathematically, and I was wondering if anybody could...
  40. L

    Dirac spinor and antiparticles

    An electron field is a superposition of two four-component Dirac spinors, one of them multiplied with a creation operator and an exponential with negative energy, the other multiplied with an annihilation operator and an exponential with positive energy. So I assume one Dirac spinor creates a...
  41. F

    Spin of single particle state of free Dirac Field

    Homework Statement Show that the state d^{\dagger}_{\alpha}(0)\mid 0\rangle describes a postrion at rest by showing that it is an eigenstate of the operators P^{\mu}, Q, J^z . Homework Equations The Fourier expansion of \psi, \psi^{\dagger}: \psi = \int \frac{d^3k}{(2\pi)^3} \frac{m}{k_0}...
  42. A

    What Does ψ_0(x) = <x|0> Represent in Dirac Notation?

    Do not solve the problem just look at the picture. http://i208.photobucket.com/albums/bb33/DanusMax/giro2_zps11d2056b.jpgWell its the end of the semester and I found out that I had only one of the required books for my undergraduate course. Anyways back to the question. As you can see in the...
  43. R

    How can boundary conditions be written for a DEQ with Dirac delta?

    Hi All, so I'm trying to tackle this DEQ: f''[x] = f[x] DiracDelta[x - a] - b, with robin boundary conditions f'[0] == f[0], f'[c] == f[c] where a,b, and c are constants. If you're curious, I'm getting this because I'm trying to treat steady state in a 1D diffusion system where...
  44. S

    How Do You Compute the Adjoint of a Quantum State in Dirac Notation?

    Homework Statement 1. Given that |ψ> = eiπ/5|a> + eiπ/4|b>, express <ψ| as a linear combination of <a| and <b|. 2. What properties characterise the bra <a| that is associated with the ket |a>? Homework Equations The Attempt at a Solution 1. <ψ| = e-iπ/5<a| + e-iπ/4<b| 2. a. The bra <a|...
  45. C

    Dirac eq gamma matrices question

    In almost all the books on field theory I've seen, the authors list out the different types of quantities you can construct from the Dirac spinors and the gamma matrices, but I'm confused by how these work. For instance, if $$\overline\psi\gamma^5\psi$$ is a pseudoscalar, how can...
  46. DiracPool

    What Insights Do Paul Dirac's Lost 1975 Lectures Offer on Quantum Mechanics?

    Hello gang, I wanted to get these lectures to you earlier but I was "temporarily indisposed," or should I say, "temporarily disposed" from the site. I guess there's only room for one bad boy in the physics community... http://www.scientificamerican.com/article.cfm?id=bad-boy-of-physics...
  47. O

    Elementary question about Dirac notation

    Hello, I'm in an introductory course about quantum computing. My math experience is fairly solid, but not very familiar with Dirac (bra-ket) notation. Just would like to clarify one thing: In a single cubit space, we have |0 \rangle , and | 1 \rangle . I understand that these form an...
  48. P

    Curved Dirac equation, Spin connection

    (1,a^2,a^2,a^2)) from the action; \mathcal{S}_{D}[\phi,\psi,e^{\alpha}_{\mu}] = \int d^4 x \det(e^{\alpha}_{\mu}) \left[ \mathcal{L}_{KG} + i\bar{\psi}\bar{\gamma}^{\mu}D_{\mu}\psi - (m_{\psi} + g\phi)\bar{\psi}\psi \right] I can show that, i\bar{\gamma}^{\mu}D_{\mu}\psi -...
  49. R

    Dirac equation continuity issue

    So I definitely believe that the continuity of the Dirac equation holds, there is one thing that annoys me, which is that c \alpha . (-i \hbar \nabla \psi ) = c (i \hbar \nabla \psi^\dagger ) . \alpha from the first part of the Dirac Hamiltonian because the momentum operator should be...
  50. P

    Dirac Equation in (-,++++) Notation

    Just to clarify in the dirac equation (i\gamma^{\mu}\partial_{\mu} -m)\psi=0 Is it equal to (-i\gamma^{0}\partial_{0}+i\gamma^{i}\partial_{i} -m)\psi=0 in (-,++++) notation?
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