# When to use ae^(ikx) quantum mechanics?

In quantum mechanics, the ae^(ikx) wave function is used to describe a particle that is localized in space. This wave function is also known as the ground state wave function. The ae^(ikx) wave function is an eigenfunction of the momentum operator, which means that it is a stationary state. The ae^(ikx) wave function is also an eigenfunction of the Hamiltonian operator. This wave function is a solution to the Schrödinger equation.

## Other related questions:

### Q: Is exp IKX is acceptable wave function?

A: Yes, exp(iKX) is an acceptable wave function.

### Q: What is exp IKX?

A: exp(IKX) is simply e (the natural number) raised to the power of IX.

### Q: How do you know if a wave function is acceptable?

A: There is no definitive answer to this question, as there is no single “correct” wave function for any given system. In general, however, a wave function is considered to be acceptable if it is physically reasonable and produces results that are in agreement with experimental data.

### Q: Is e IKX square integrable?

A: $\int_0^1 e^{-IKX} \, dX$

$\int_0^1 e^{-IKX} \, dX = \left[ \frac{e^{-IKX}}{-IK} \right]_0^1$

$\int_0^1 e^{-IKX} \, dX = \left[ \frac{e^{-IK}}{-IK} – \frac{1}{-IK} \right]$

$\int_0^1 e^{-IKX} \, dX = \frac{e^{-IK}}{IK} – \frac{1}{IK}$

$\int_0^1 e^{-IKX} \, dX = \frac{1}{IK} \left( e^{-IK} – 1 \right)$

$\int_0^1 e^{-IKX} \, dX = \frac{1}{IK} \left( e^{-IK} – 1 \right)$

Thus, $e^{-IKX}$ is integrable on