Yup, seems like it. It is rather odd of them to do that though; usually we like -∞ to ∞ bounds because they allow us to use the Gaussian integration formula.marineric said:I think I got it. The solutions manual integrated from 0 to ∞, and multiplied by 2 because of symmetry (to get the -∞ to 0 part)
A wave function is a mathematical description of a quantum system, which describes the probability of finding a particle in a certain state at a given time. It is important because it allows scientists to predict the behavior of particles at the microscopic level, which has important applications in fields such as quantum mechanics and atomic physics.
Normalizing a wave function means adjusting its values so that the total probability of finding a particle in any possible state is equal to 1. This ensures that the wave function accurately represents the behavior of the particle and follows the laws of quantum mechanics.
Normalizing a wave function can be difficult because it involves complex mathematical calculations, such as integration and complex numbers. Additionally, the wave function may have multiple variables and conditions that need to be satisfied in order to be properly normalized.
If a wave function is not properly normalized, it can lead to incorrect predictions of the behavior of particles. This can result in errors and inconsistencies in scientific research and applications, and can also violate the fundamental principles of quantum mechanics.
Scientists use mathematical techniques and equations, such as the normalization condition, to determine if a wave function is normalized. This involves calculating the total probability of finding a particle in all possible states and ensuring that it equals 1. If the wave function does not satisfy this condition, it is not normalized.