Questions tagged [operators]

Questions about using or composing operators--functional mappings from one state or vector space to another.

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229 views

How may I define e.g. Tilde[x,y] to have certain properties?

I would like to define, e.g., the Tilde[x,y] operator to have certain properties, and then investigate whether certain expressions involving that operator are True or not. For example, if I specify ...
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1answer
78 views

Lowering operator for spherical harmonics [duplicate]

I need to be able to generate all of the $ l=2 $ spherical harmonics using the lowering operator. The specific question is listed below. Any assistance would be much appreciated! Thanksenter image ...
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1answer
148 views

Partial trace and Partial Transposition of a matrix easily? [closed]

Could someone help me to understand as to how to compute the partial trace and partial-transposition of an arbitrary matrix? I mean, is there any code to carry out these operations in Mathematica? ...
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1answer
51 views

Symbollic integration and differentiation of operated functions

This question is a continuation of this one. I used the answer provided in the previous question to write this code ...
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1answer
457 views

Symbolic matrix calculation [closed]

I have question about a matrix calculation like $\mathbf{b}^{t}\,\Sigma\,\mathbf{b}$, where $\Sigma$ is a 7 by 7 matrix, and $\mathbf{b}$ is vector of 7 elements, and each element in the vector $\...
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1answer
139 views

What's wrong with my implementation on CountryData

I was wondering, *for which countries is the proportion of Phone line users to population greater than or equal to that of the United States?* This is what I inputted below, but the list of countries ...
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1answer
59 views

How to substitute integral operators into polynomials?

Suppose I have a polynomial $a_0+a_1 f(x,t) + a_2 f(x,t)^2 + ....$. In code, a0 + a1 y + a2 y^2 + a3 y^3 /. y :> Integrate[Subscript[y, k] E^(I k y), k] <...
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1answer
42 views

Performing a simple operation with operators [closed]

I have a map defined as $\qquad \Phi(X) = a^2\, Tr[X] |0\rangle \langle 0| + b^2\, Tr[X] |1\rangle \langle 1| + a\,b\, Tr[\sigma_z X] |0\rangle \langle 1| + a\,b\, Tr[\sigma_z X] |1\rangle \langle ...
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1answer
80 views

How to program Mathematica to do the differential operator calculation

I want to create a surface Laplacian under the spheroidal coordinates, Now, I already have the surface gradient defined, but I don't know how to find the Laplacian. Since the surface gradient is too ...
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1answer
118 views

How to efficiently exponentiate a differential operator with non-commuting terms, acting on an infinite series?

My question is related to this one, but I am more explicit with the form of the operator in the exponential and the function $f$. Let us have the expression: $$ e^{\mathrm{i} \left( f(x)(\hat{q} \...
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1answer
487 views

what do those signs #1, #1^2, #1^3, & mean here? [duplicate]

I have read common pitfalls page and the documentation page but I still don't understand what do those signs mean here? ...
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1answer
185 views

Define action of noncommutative product of operators

I have objects wrapped with head fv. So they are things like fv[{1, 2}, {3, 4}, {5, 6}] I then defined two operators, a and <...
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1answer
71 views

Divergence and gradient operators in two dimensions

Divergence of a vector $\mathbf{a}$ can be numerically written as, \begin{eqnarray} \nabla \cdot \mathbf{a} \approx \sum_{i=0-9} w_i\mathbf{a(x+c_i)}\cdot \mathbf{c}_i \end{eqnarray} The lattice ...
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2answers
55 views

Sum over integer partition with variable function argument

Define $$\hat{X}(Y) = [X,Y] $$ I have known matrices $S_i$ and $V$. I am trying to use Mathematica to define a function which calculates $$ \sum_{\substack{n_1, \ldots, n_k>1\\ n_1+\ldots n_k = ...
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2answers
73 views

A list of operators in the For cycle

I'm pretty sure that analogous questions have been asked here a zillion of times, but... I think it is pretty straightforward from the code what I expect it to give: ...
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1answer
63 views

How can I define a derivation in Mathematica?

I would like to define a derivation in Mathematica. As an example something like this: for an operator O and operators $A,B$ in a two dimensional vector space with $$ O \times A = a \\ O \times B = b \...
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3answers
200 views

Calculating bracket operations [closed]

Is there a way to calculate commutation relations in Mathematica? For example, let's say I want to compute ; how can this be done?
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1answer
81 views

How to put a levelspec in operator form? [closed]

All variable argument functions need Function wrapped around them in operator form, but is there any other way to achieve this: ...
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0answers
21 views

How to transform polynomial to differential operator?

How to transform the multiariate polynomial to corresponding differential operator? For instance, for a polynomial $ \frac{1}{2} z_1^2 z_3^6 $ is the goal operator $ \frac{\partial ^8}{\partial ^2x_1\...
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33 views

Implicit definition of a coordinate in differential equation [duplicate]

I would like to solve the following differential equation $\frac{d^2 \psi(r_*)}{dr^2_*} + (\omega^2 - V(r)) \psi(r_*)=0$ and the boundary conditions are $\psi(\inf) = \psi(-inf) = 0$. The problem is ...
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0answers
38 views

How to compute gauge variation of expression?

Suppose I have a symmetric tensor field $h_{\mu\nu}$ I want to implement somehow the following gauge variation of this tensor field as follows $\delta h_{\mu\nu} = \nabla_{\mu}\epsilon_{\nu} + \...
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1answer
58 views

Multiply function-valued matrices

I would like to create a notebook for calculations in supersymmetric quantum mechanics. The basic building blocks are two functions (or maybe better: operators): ...
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0answers
36 views

Defining a function through an ODE containing unspecified operators

I want to do some algebra using a function only defined through a DE containing unspecified operators. The DE is $$ \partial_zu(z) = \left[\hat{D}+\hat{N}(z,u)\right] u(z). $$ Here $u$ lives in ...
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1answer
106 views

How to construct — based on physics-type notation — a magical simplex $\mathcal{W}$ of bipartite qutrits?

I have a short Mathematica program: ...
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0answers
125 views

Commutator of differential operators

Let $P_x = \frac{\hbar}{i}\frac{d}{dx}$, after specifying the commutator relation symbolically $[X, P_x] = i\hbar$, I can ask Mathematica to calculate commutator algebra. My question: is there a way ...
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0answers
40 views

How do you treat gradient as a vector? [duplicate]

I need to express $\nabla = (\partial_x,\partial_y,\partial_z)$ as a vector, so that I can compute the differential operator given by $A\cdot\nabla$ (where here $A$ is a 3x3 matrix) using Mathematica. ...
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0answers
54 views

Non-commutative multiplication sign and constant treatment

By default, non-commutative multiplication behaves as (-W) ** (4 R) //FullForm ...
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0answers
83 views

How to use multiple placeholders to define a function that operates on special functions.

I am trying to understand if and how I can use multiple placeholders in order to define a function that will perform more than one operations on special functions; more accurately, sums, products, etc ...
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0answers
63 views

How to create operator variables and lists of operators?

I want to know if it is possible to create a variable that is an operator. (Please note I only started programming Mathematica today) For example, the partial operator $\partial_x$ i.e. ...
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0answers
85 views

How to define a product on formal power series (pseudo-differential operators)?

I am used to working with the set of (algebraic) pseudo-differential operators, which consists of formal power series in the symbol $D$ (differentiation operator) of the form $$X = \sum_{j=-\infty}^n ...
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0answers
173 views

Defining a complex partial differential operator

I tried to define a partial differential operator using this code ...
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0answers
233 views

Defining a del operator [duplicate]

I understand the Grad function is a mean to taking the gradient of an arbitrary function. However, I'd like to define the Del ...
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0answers
326 views

Non commutative products and scalars

Say I have an expression such as $$a.(\alpha b)$$ where $a$ and $b$ are non-commutative operators, but $\alpha$ is simply a scalar. How do I tell Mathematica to treat $\alpha$ as a scalar and "pull" ...
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0answers
95 views

How to define the tangent gradient operator? [duplicate]

I would like to define a new differential operator that is the tangent gradient for a curve $\Sigma$. This is defined as $$\nabla_\Sigma=\mathbf{P}\nabla$$ where $\mathbf{P}$ is the projection ...
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1answer
66 views

odd matrix operation [closed]

This is for the case of a 10 x 10 matrix. I have the matrix ...