d) Calculate the commutator where the function m

Question

d) Calculate the commutator $\left [ p,e^{ik0x} \right ]$ where the function $e^{ik0x}$ may be expanded as: $e^{ik0x}=\sum _{n=0}^{\infty }\frac{(ik_0x)^n}{n!}$

13 Mar 2024

Answer :

Word Count : 288

To calculate the commutator $[p, e^{ik_0x}]$, we need to know that $p$ represents the momentum operator and $e^{ik_0x}$ is a function that can be expanded as:

\[
e^{ik_0x} = \sum_{n=0}^{\infty} \frac{(ik_0x)^n}{n!}
\]

The commutator of two operators $A$ and $B$ is defined as $[A, B] = AB - BA$.

Let's proceed with the calculation:

1. **Commutator $[p, e^{ik_0x}]$:**

\[
\begin{align*}
[p, e^{ik_0x}] &= p \cdot e^{ik_0x} - e^{ik_0x} _________ ___ _____ ______ _______ __________.
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