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

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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 ...
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107 views

How to construct custom operators with precedence?

I need to combine data structures in operations analogous to addition, subtraction, multiplication and division (and more). I need more than one operation of each type, i.e. more than one method of ...
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46 views

Products of Differential Operators

I have a differential equation defined as the product of operators which I want to expand out into a polynomial in powers of $z\frac{d}{dz}$ $\prod_{n=1}^p(z\frac{d}{dz}+a_n)$ However when I try to ...
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134 views

Defining an operator

Let s be a positive integer and let DifferenceDelta be this function with step = 1. Define ...
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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 ...
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45 views

Operator product

I have this problem: I define the gradient operator as: gradiente = {D[#, x] &, D[#, y] &, D[#, z] &} Now, if I want to apply the operator on a ...
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75 views

Applying the square root of operator on polynomial functions

I am trying to apply an "operation" on polynomial functions: apply the operator $(\frac{\partial f}{\partial x}-y\frac{\partial f}{\partial z})^2+(\frac{\partial f}{\partial y}+x\frac{\partial ...
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Computing integrals with differential operator

I've to compute this expression $$ \hat{H} = \frac{1}{4}g_2\int d^3R\int d^3r\ \bar{\Psi}(\vec{R}+\frac{\vec{r}}{2})\bar{\Psi}(\vec{R}-\frac{\vec{r}}{2})\left[ \delta(\vec{r})\nabla_{\vec{r}}^2 ...