Operators Definition and 1000 Threads

I heard something about the well known Leibniz notation of calculus, and I thought that you guys would be able to tell me if it's a load of hogwash or not. The geist of it is this: \mathrm d and \int are actually operators, with \mathrm d being an operator that creates an infinitesimal from a...

Hi all, Trying to write an SQL query for the Sloan Digital Sky Survey that uses the NOT operator, and failing miserably. Basically, I'm making photometric cuts in 4-d colour space, and I currently have a selection of inequalities that select enclosed regions of colour space. However, I...

\hat{x} = \left(\frac{\hbar}{2wm}\right)^{1/2}(\hat{a} + \hat{a}^{+}) \hat{p} = -i\left(\frac{\hbar wm}{2}\right)^{1/2}(\hat{a} - \hat{a}^{+}) I'm trying to demonstrate that \hat{H} = (\hat{a}^{+}\hat{a} + \frac{1}{2})\hbar w where \hat{H} = \frac{1}{2m} \hat{p}^{2} +...

Hey i was wondering if someone could help me express this using standard binary operators. f(x,y,z)=\frac{max(0, (x-y) )}{z} i.e. Eliminate the max() function and write it using proper math. EDIT: max(a,b) simply chooses the largest value of the two variables.

I was just messing around on another problem I was trying to solve for someone in the homework forums when I stumbled on this: If we denote the n-th derivative the same way we do for exponents, eg the second derivative of f will be denoted by f^2, and the original function as its zero-th...

When we set the raising and lowering operators for spin to be S_{\pm} = S_x \pm i S_y, what convention are we following (i.e. why is the first term taken to be S_x and the second taken to be S_y)?

[SOLVED] Expectation Values of Spin Operators Homework Statement b) Find the expectation values of S_{x}, S_{y}, and S_{z} Homework Equations From part a) X = A \begin{pmatrix}3i \\ 4 \end{pmatrix} Which was found to be: A = \frac{1}{5} S_{x} = \begin{pmatrix}0 & 1 \\ 1 & 0...

I have two problems and I don't know what they want to tell. Please tell me what do you think 1. We define operator L[x]=a(t)\ddot{x}+b(t)\dot{x}+c(t)x in C^{2}(I) function space. Proof that \frac{\partial}{\partial\lambda}L[x]=L\left[\frac{\partial x}{\partial\lambda}\right]. ¿What do you...

Is it true, that if in Hilbert space, operators T and S satisfy (Tf|f)=(Sf|f) for all f in H, then T=S? I think it is clear, that if (Tf|g)=(Sf|g) is true for all f and g in H, then T=S, but I'm not sure if it is sufficient to only allow g=f.

This isn't exactly a part of any problem, but a part of a generic principle. I don't understand the use of raising and lowering operators. L_{^+_-}=\hbar e^{^+_- i l \phi}({^+_-}\frac{\partial}{\partial \theta}+ i cot \theta \frac{\partial}{\partial \phi}) So how does one use L_{^+_-}Y_l^m...

I wonder if someone could examine my argument for the following problem. Homework Statement Using the relation \widehat{x}^{2} = \frac{\hbar}{2m\omega}(\widehat{A}^{2} + (\widehat{A}^{+})^{2} + \widehat{A}^{+}\widehat{A} + \widehat{A}\widehat{A}^{+} ) and properties of the ladder operators...

in the quantum mechanical operators : why : [YPz,YPx]=0 [ZPy,ZPy]=0 [X,Py]=0 [Y,Pz]=0 [Z,Py]=0

Homework Statement This is a problem about differential operators, but I don't really get the notation used. I have L1 = (d/dx + 2) and L2 = (d/dx - 1) Find L1(xe^-2x) Show that L1L2 = L2L1 and find L1L2 in terms of d/dx, d2/dx2, etc. Homework Equations The Attempt at a...

Hi Homework Statement We're given the operators Lx, Ly and Lz in matrix form and asked to show that they have the correct eigenvalues for l=1. Obviously no problem determining the values and Lz comes out right, however we've never actually seen the e.v.s for Lx and Ly. Homework...

So I was reading from my quantum book (Gasiorowicz) and I ame across this sentence: [p^2, x] = p [p, x] + [p, x] p = \frac{2\hbar}{i} p I don't understand this. I know that p = -i \hbar \frac{\partial}{\partial x} , but I can't see how to get that expression...I just come up with...

Whats the intuition behind the concept of current operator in QFT and PP. For example i know that the charge operaor which correspond to space integral of J-o when acted upon a fock space of the field of given type gives the total charge in the field but what about the remaining components...

Homework Statement Obtain the angular momentum operators L_{x} and L_{y} in the basis of functions Y^{\pm1}_{1}(\theta,phi} and Y^{0}_{1}(\theta,phi}[/itex] in Lz representation2. The attempt at a solution To calculate the matrices for the Lx and Ly operators, do i simply have to take the...

Can operators describe a single or many measurements at a single time? i.e. a stern-gerlach atom deflection experiment where we can measure "up" deflection and "down" deflection or just "up" deflection. I think I'm pretty confused..

I have some questions about the properties of a Hermitian Operators. 1) Show that the expectaion value of a Hermitian Operator is real. 2) Show that even though \hat{}Q and \hat{}R are Hermitian, \hat{}Q\hat{}R is only hermitian if [\hat{}Q,\hat{}R]=0 Homework Equations The...

Question: Is the Fourier Transform of a Hermitian operator also Hermitian? In the case of the density operator it would seem that it is not the case: \rho(\mathbf{r}) = \sum_{i=1}^N \delta(\mathbf{r}-\mathbf{r}_i) \rho_k = \sum_{i=1}^N e^{-i\mathbf{k} \cdot \mathbf{r}} I have a hard...

Let's say we have a symmetric potential, in position representation V(x)=V(-x) and let P be the parity operator. Then quite clearly PV=VP but I was told the stronger statement V=PV is not true, but I thought V=\int_{-\infty}^{\infty} V\left|x\right\rangle\left\langle x \right| dx (where I...

I hope this is the forum to ask this question. We all know that the eigenvectors of a Hermitian operator form an orthonormal basis. But is the opposite true as well. Are the vectors of an orthonormal basis always the eigenvectors of some Hermitian operator? Or do we need added restrictions to...

I thought that I had angular momentum very well understood, but something has been giving me problems recently. It is often stated in textbooks and webpages alike, that the angular momentum ladder operators defined as J_{\pm} \equiv J_x \pm i J_y Then the texts often go on to say that these...

I ve been trying to derive this for some time now. The rule is similar to the one for simple math derivatives. d/dx(A^B^)=dA^/dx B^ + A^ dB^/dx Is the derivation on similar lines. Any directions??

Homework Statement Consider the following operators a) Reflection: \hat{I}\Psi(x)=\Psi(-x) , x\in(-\infty,\infty) b) Translation: \hat{T_{a}}\Psi(x)=\Psi(x+a), x\in(-\infty,\infty) c) \hat{M_{c}}: \hat{M_{c}}\Psi(x) = \sqrt{c}\Psi(x) d) \hat{c}\Psi(x)= (\Psi(x))^* e)...

Homework Statement I understand, mathematically, that the translation operator (both for infinitesimal and finite translations) can be written as a function of the momentum operator. It is said then that momentum "generates" translation. Similiary, the rotation operator can be written as a...

Hello all, I've been thinking about the connection between commutativity of operators and uncertainty. I've convinced myself that to have simultaneous eigenstates is a necessary and sufficient condition for two observeables to be measured simultaneously and accurately. It's also clear...

How can we show \left[\hat{H},\hat{x}\right]=\frac{-i\hbar}{m} \hat{p_{x}} ?

Homework Statement Show that if \Omega is an hermitian operator, and \varphi and \psi are (acceptable) wavefunctions, then then \int \phi^{*} \Omega \psi dz = \int \psi (\Omega \phi)^{*} dz Homework Equations Consider the wave function \Psi = \phi + \lambda\psi The Attempt at a...

why i\hbar(\partial/\partialt+i\Omega)=i\hbarexp(-i\Omegat)\partial/\partialtexp(i\Omegat)

I have a problem with deriving another result. Sorry I am new to this field. Please see the attached PDF - everything is there.

Homework Statement I am trying to learn from Srednicki's QFT book. I am in chapter 2 stuck in problem 2 and 3. This is mainly because I don't know what the unitary operator does - what the details are. Starting from: U(\Lambda)^{-1}U(\Lambda')U(\Lambda)=U(\Lambda^{-1}\Lambda'\Lambda) How does...

I posted this is in the QM section but maybe here would have been better. I don't think it is a hard question for anyone who knows QM: https://www.physicsforums.com/showthread.php?t=181220

The context of this question is chemistry but I think that it contains enough quantum mechanics to warrent posting it here instead of in the chemistry forum. Go to section 2.1.1 at the following site: http://tesla.ccrc.uga.edu/publications/papers/qrevbiophys_v33p371.pdf I am confused...

Why must the ladder operators be \sqrt{\dfrac{m\omega}{2\hbar}}(x+\dfrac{ip}{m\omega}) and \sqrt{\dfrac{m\omega}{2\hbar}}(x-\dfrac{ip}{m\omega})? What is the method that obtain them from schrodinger Equation? And why we know that they are creation and anihilation operator?

i am having trouble with understanding the physical significance of these two operators.

This is very exciting. I have wondered about this merely as a spectator, because e.g. AFAIK the spinfoam formalism has not confirmed that about the geometric operators. What they say is that discrete spectrum HAS NOT BEEN PROVEN yet for the geometric operators, so it could go either way. Also I...

I'm a newcomer here... so I introduce myself: I've just completed my BS in physics and joining M.Sc... I've interested to take specialisation in Quantum mechanics and will continue in theoretical physics in the future... I'm facing problems understanding the algebra of operators...

let be the operator involving an infinite-dimensional ODE f( \partial _{x}) y(x)=h(x) then if h(x)=0 i make the ansatz y(x)=e^{ax} so \sum_{\rho } e^{x\rho} f(\rho) =0 for h(x) different from '0' we construct an orthonormal basis with the solutions given above to give an...

helow guys i am atif elahi from pakistan i have some problem in topic operators in quantum mechanics can you people help me i shall be very thankful to you thanks

I'm reading an article where there are an atom with two states, let's call them |0> and |1>. Then the writer defines an operator by |0><1| I know how this operator works in the bra ket notaion, but how does it work, if I want to use it in the position basis? Someone told me that I just...

What for do we need operators in QM. Where is the complete state description of a quantum object?

Suppose T: X -> Y and S: Y -> Z , X,Y,Z normed spaces , are bounded linear operators. Is there an example where T and S are not the zero operators but SoT (composition) is the zero operator?

Defining the state | \alpha > such that: | \alpha > = Ce^{\alpha {\hat{a}}^{\dagger}} | 0 >\ ,\ C \in \mathbf{R};\ \alpha \in \mathbf{C}; Now, | \alpha > is an eigenstate of the lowering operator \hat{a}, isn't it? In other words, the statement that \hat{a} | \alpha >\ =\ \alpha | \alpha >...

Homework Statement why is the spectrum of the unitary operator the unit circle? Homework Equations i know that U^(-1)=U* and i know this makes U normal i also know that normal means UU*=U*U The Attempt at a Solution i know that from spectral theory there is some lambda in the...

Homework Statement Prove that any square triangular matrix with each diagonal entry equal to zero is nilpotent The Attempt at a Solution Drawing out the matrix and multiplying seems a little tedious. Perhaps there is a better way? Is there another way to do this without assuming that the...

Homework Statement It is possibly not a homework problem.However,to do a homework problem,I require this: Boas writes the effect of Ladder operators on y_n that satisfies y"_n-x^2y_n=-(2n+1)y_n,n=0,1,2,3... (D-x)(D+x)y_n=-2ny_n (D+x)(D-x)y_n=-2(n+1)y_n Then,she proved...

Here's a question about inequivalent representations of the CCRs... For a given Hilbert space representation, what is it that determines which set of field operators \phi(x), or \phi(f) if we want to get rigorous a la Wightman, gives us THE field operators for that representation. For example...

I have worked out how the connection coefficients enter into the expression for the Laplacian, for example, in different coordinate systems. Does anyone have general expressions for how the coefficients enter into other expressions such as divergence and curl and grad and so on? Thanks in...

Hello , This is regarding the equality of nullity between A and PAP(inverse). If my understanding is correct then the thing should be according to the diagram belowV---------------->R1(isomorphic to V) | | | | \/ \/...