Questions tagged [operators]

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

21 questions with no upvoted or accepted answers
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Operator which can be interpreted as binary and unary

I'm a bit lost with the way how e.g. the + operator is implemented in Mathematica as binary (infix) and unary (prefix) operator depending on the context, since I would like to define a similiar ...
4
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0answers
681 views

Is it possible to simplify an expression in vector form, which involves crossproduct and dot product?

I often need to simplify expressions involving cross product and dot product, for example: f = Dot[Cross[Cross[p1 - p, e1], Cross[p2 - p, e2]], Cross[p3 - p, e3]] ...
2
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1answer
149 views

Wick's theorem for Gaussian stochastic variables

I wonder whether there exists a clever way to implement Wick's theorem for Gaussian stochastic variables $\eta_{j_{i}}$ (with $\langle \eta_{j_{i}}\rangle=0$ for $\forall i$) which in general states: ...
2
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0answers
57 views

Defining the Distributive Depth of an Operator

I am working on defining the relations between Bras and Kets in Mathematica, and I am using the CircleDot operator to represent multiplication. I seem to have some trouble defining how operations on ...
1
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0answers
66 views

Superposition of the differential operators

My problem can be easily solved without Mathematica, however, I am curious how to do it in Mathematica. Moreover, I can be stuck with a similar, but more cumbersome problems in the future. Following ...
1
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0answers
53 views

Operator on a multivariable function in a sum

I need to define an operator that does as follow for any function $h_m$. $\qquad O[h_m](k,M,b,l_{max})=\sum_{l\neq (0,m)}^{l_{max}}il \left (h_l(k,M,b,l_{max}) b_{m-l}(k)- c_l\partial_k h_{m-l}(k,M,...
1
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0answers
69 views

How can I realize operator $\frac{D}{e^D-1}$ in Mathematica?

Especially if it is applied to an integral of a function. So, I need for a given function f[t] the following: $\frac{D}{e^D-1} \int_0^t f(t)dt |_{t=\omega}$
1
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0answers
50 views

Operator Splitting and Taylore series

I am not a user of mathematica so I am not sure if what I want to do is possible. Imagine I have the following cauchy problem: $$\frac{dw}{dt} = F(t, w(t)) = f1(w(t), t) + f2(w(t), t)$$ where I have ...
1
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0answers
213 views

Defining an operator

Let s be a positive integer and let DifferenceDelta be this function with step = 1. Define <...
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0answers
79 views

Parallelizing an associative binary operation

I have an associative binary operation '.', which I often use in this sort of way: result = expr1 . expr2 . expr3 . expr4 The ...
0
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0answers
23 views

Implicit definition of a coordinate in differential equation

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 ...
0
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0answers
32 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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35 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 ...
0
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1answer
92 views

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

I have a short Mathematica program: ...
0
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0answers
102 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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48 views

Non-commutative multiplication sign and constant treatment

By default, non-commutative multiplication behaves as (-W) ** (4 R) //FullForm ...
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0answers
74 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
61 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. ...
0
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0answers
81 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 ...
0
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0answers
165 views

Defining a complex partial differential operator

I tried to define a partial differential operator using this code ...
0
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0answers
287 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" ...