Dirac Definition and 859 Threads

Hi Guys, I am facing a problem playing around with some operators and Kets, would like some help! I have \langle \Psi | A+A^\dagger | \Psi \rangle .A Could someone simplify it? Especially is there a way to change the last operator A into A^\dagger? The way I thought about this is...

I'm looking through my lecture notes, (studying relativistic corrections/perturbation theory using hydrogen), and I seem to have a mind block with one of the equations (the last one from the 3 in the middle). I know that the kinetic energy and coulomb potential has been subbed in for the...

Is there a time domain function whose Fourier transform is the Dirac delta with no harmonics? I.e. a single frequency impulse

So part of the idea presented in my book is that: div(r/r3)=0 everywhere, but looking at this vector field it should not be expected. We would expect some divergence at the origin and zero divergence everywhere else. However I don't understand why we would expect it to be zero everywhere but...

Hello I am trying to solve the dirac equation. I want to solve the dirac eq say for 2 particle system. therefore i request you to please suggest me the book or some material. Thank you

My layman's intuition tells me that wave packets normally spread out in space and disperse, except in special circumstances. Photons don't behave like that. In The Principles of Quantum Mechanics, pp 124-125, Dirac discusses the equations of motions of a photon wave packet. He says...

Casual talk. Constrained Hamilton systems. Dirac-Poisson brackets. Casual talk. Constrained Hamilton systems. Dirac-Poisson brackets. Hi guys, I think I have finally succeeded in understanding the ideas which Dirac explained in the two first chapters of his book "Lectures on Quantum...

Hi, I recently attended several lectures on the topic of neutrino astrophysics. I wanted to verify some of the fact that I gleaned for them, specifically about the Dirac vs Majorana nature of neutrinos. 1) The most basic fact first. If a neutrino is Dirac in nature, then it has 3 flavors...

How can I find the derivative of a step function?

I'm having a problem writing the third Dirac current eq. $$1 = \int ψ^t \gamma^0 \gamma^2 ψ$$ which should come out as $$1 = \int i ψ^0 ψ^3 - i ψ^1 ψ^2 + i ψ^2 ψ^1 - i ψ^3 ψ^0$$ By inspection the first and last terms add to zero and the second and third terms add to zero, so the integral...

On page 86 of The Principles of Quantum Mechanics, Dirac left me in his dust. I quote: [u_{1},v_{1}](u_{2}v_{2}-v_{2}u_{2})=

hi guys, I wonder if I have fully understood the Fermi Dirac statistics properly, but I have a question on it regarding its application in the white dwarf research. I read the Fermi energy is applicable for T=0, now if the core of a white dwarf is too hot then how can we apply the Fermi Dirac...

Hi guys, I m reading some theoretical physics paper that requires knowledge of dirac notation if someone could point me out to a good tutorial on it I come from a math background but I am studying this paper with my supervisor.

Is it possible to solve a differential equation of the following form? $$\partial_x^2y + \delta(x) \partial_x y + y= 0$$ where ##\delta(x)## is the dirac delta function. I need the solution for periodic boundary conditions from ##-\pi## to ##\pi##. I've realized that I can solve this for some...

How to calculate ##\int^{\infty}_{-\infty}\frac{\delta(x-x')}{x-x'}dx'## What is a value of this integral? In some youtube video I find that it is equall to zero. Odd function in symmetric boundaries.

I am self studying the 17th Chapter of "Mathematical Methods for Physics and Engineering", Riley, Hobson, Bence, 3rd Edition. It is about eigenfunction methods for the solution of linear ODEs. Homework Statement On page 563, it states: "As noted earlier, the eigenfunctions of a...

Homework Statement This isn't really a problem so much as me not being able to see how a proof has proceeded. I've only just today learned about Dirac notation so I'm not too good at actually working with it. The proof in the book is: |Z> = |V> - <W|V>/|W|^2|W> <Z|Z> = <V - ( <W|V>/|W|^2 ) W|...

I would expect that the Heisenberg equation of motion for the Dirac field would yield the Dirac equation. Indeed, these lecture notes claim it as a fact in eq 7.7 but without proof. My trouble is that I know the anti-commutation rules for the Dirac field but I don't know how to calculate the...

Homework Statement This complies when I type it in my Latex editor, but not on here. If you could either let me know how to fix that or copy and paste what I have into your own editor to help, that'd be great. Thanks! While Ryder is setting up to derive a transformation rule for Dirac...

I believe I understand the mathematical derivation of the Dirac equation. I understand how the four 4X4 matrices, and their relation to the 2X2 Pauli Matrices, arise from that derivation. I understand that the 3 spin observables for Fermions are ALSO represented by the 3 Pauli Matrices...

Quantum Mechanics using Index notation. Is it possible to do it? I really don't get the Dirac Notation, and every-time I encounter it, I either avoid the subject, or consult someone who can read it. There doesn't seem to be any worthy explanation about it, and whenever I ask what is the Hilbert...

How do i derive the Dirac equation from L_{dirac} = \overline{ψ}_α [i(γ^μ)_{αβ} - m]ψ_β ?. I can get it for the \overline{ψ} , but I'm having trouble deriving it for ψ .

Is there any way to write the Dirac lagrangian to have symmetric derivatives (acting on both sides)? Of course someone can do that by trying to make the Lagrangian completely hermitian by adding the hermitian conjugate, and he'll get the same equations of motion (a 1/2 must exist in that...

In the standard QFT textbook, the Hermitian conjugate of a Dirac field bilinear \bar\psi_1\gamma^\mu \psi_2 is \bar\psi_2\gamma^\mu \psi_1. Here is the question, why there is not an extra minus sign coming from the anti-symmetry of fermion fields?

Hello Homework Statement From the expression of the partition function of a fermi dirac ideal gas ln(Z)=αN + ∑ ln(1+exp(-α-βEr)) show that S= k ∑ [ <nr>ln(<nr>)+(1-<nr>)ln(1-<nr>) Homework Equations S=k( lnZ+β<E>) <nr>=-1/β ∂ln(Z)/∂Er <E>=-∂ln(Z)/∂β The Attempt at a Solution I...

I have a Gaussian distribution about t, say, N(t; μ, σ), and a a Dirac Delta Function δ(t). Then how can I compute: N(t; μ, σ) * δ(t > 0) Any clues? Or recommender some materials for me to read? Thanks!

Sorry if the question seems naive but if we have the Dirac delta function delta(x-y) is it the same as delta(y-x)?? Or there are opposite in sign? And why ? Thank you for your time

I must admit that I have never had a great familiarity with the Dirac equation. No matter how many times I study it, I get bogged down in the algebra and never seem to get a good understanding of it. So here's a few questions in my mind at the moment. I am referring here to the Dirac equation as...

I usually know how to manipulate bras and kets. But I probably found difficulty because of the double summation. How did Sakurai manage to go from the second line to the ird line in the attachment? SECTION 4.4 in Sakurai.

Homework Statement This makes intuitive sense to me, but I am getting stuck when trying to read the Dirac notation proof. Anyway, the author (Shankar) is just demonstrating that the product of two operators is equal to the product of the matrices representing the factors. Homework Equations...

I am not understanding something from my textbook. This is related to Fermi's Golden rule. It's about what happens when the matrix element of the perturbation H' ends up being a Dirac delta for chosen normalization. Here is Fermi's Golden rule. \Gamma_{ba} = 2\pi \left|\langle b \mid H'\mid a...

Hi all! I was reading up on the Klein paradox in Itzykson & Zuber's Quantum Field Theory (but I think this is a pretty standard part that's probably present in most QFT textbooks) and on page 62 they have a pretty straight forward solution to the Dirac equation with a step potential. I've...

Hi, This is probably a trivial question, but I just wanted to check my understanding. Is the following expression for the Dirac Lagrangian correct...

Homework Statement Consider the function \delta_{\epsilon}(x) defined by \delta_{\epsilon}(x)=\begin{cases} 0\text{,} & x<-\epsilon\text{,}\\ \frac{3}{4\epsilon^{3}}(\epsilon^{2}-x^{2})\text{,} & \epsilon\leq x\leq\epsilon\text{,}\\ 0\text{,} & \epsilon<x\text{,} \end{cases} (b) Consider a...

If you ask me define Dirac delta function, i can easily define it and prove its properties using laplacian or complex analysis method. But still i don't understand what is the use of DIRAC DELTA FUNCTION in quantum mechanics. As i have done some reading Quantum mechanics from Introduction to...

Question and symbols: Consider a state|ε> that is in a quantum superposition of two particle-in-a-box energy eigenstates corresponding to n=2,3, i.e.: |ε> = ,[1/(2^.5)][|2> + |3>], or equivalently: ε(x) = [1/(2^.5)][ψ2(x) + ψ3. Compute the expectation value of momentum: <p> = <ε|\widehat{}p|ε>...

Homework Statement Hey guys. So here's the situation: Consider the Hilbert space H_{\frac{1}{2}}, which is spanned by the orthonormal kets |j,m_{j}> with j=\frac{1}{2}, m_{j}=(\frac{1}{2},-\frac{1}{2}). Let |+> = |\frac{1}{2}, \frac{1}{2}> and |->=|\frac{1}{2},-\frac{1}{2}>. Define the...

Hello! By manipulating Maxwell's equation, with the potential vector \mathbf{A} and the Lorentz' gauge, one can obtain the following vector wave equation: ∇^2 \mathbf{A}(\mathbf{r}) + k^2 \mathbf{A}(\mathbf{r}) = -\mu \mathbf{J}(\mathbf{r}) The first step for the solution is to consider a...

Homework Statement I need to prove for arbitrary functions φ(x) that: \lim_{\lambda \to 0} \int_{-\infty}^{\infty} \frac{1}{\sqrt{2 \pi} \lambda} exp\left( \frac{-x^{2}}{2 \lambda^{2}} \right) \varphi(x) dx = \varphi(0), which, in the sense of distributions is basically the delta...

Hello. I would like to ask something that will help me understand a little better how we work with Dirac spinors' inputs... I know that the dirac equation has 4 independent solutions, and for motionless particles, the (spinor) solutions are: u_{+}=(1,0,0,0)^{T} electron +1/2...

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...

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'...

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...

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...

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...

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...

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...

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) =...

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...

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...