Why didn 't we define the derivative matrix on a grid through the familiar asymmetric derivative begin equation frac d f(x) d x lim Delta x ightarrow 0 frac f(x Delta x) f(x) Delta x tag 2 90 end equation What are its eigenvalues What happens when it is exponentiated ...

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Why didn't we define the derivative matrix on a grid through the familiar asymmetric derivative: [begin{equation*}frac{d f(x)}{d

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Why didn't we define the derivative matrix on a grid through the familiar "asymmetric" derivative:

\[\begin{equation*}\frac{d f(x)}{d x}=\lim _{\Delta x \rightarrow 0} \frac{f(x+\Delta x)-f(x)}{\Delta x} ? \tag{2.90}\end{equation*}\]

What are its eigenvalues? What happens when it is exponentiated?

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Quantum Mechanics A Mathematical Introduction

ISBN: 9781009100502

1st Edition

Authors: Andrew J. Larkoski

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Question Posted: Mar 30, 2024 10:00 PM

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Why didn't we define the derivative matrix on a grid through the familiar asymmetric derivative: [begin{equation*}frac{d f(x)}{d

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Quantum Mechanics A Mathematical Introduction

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