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Chapter 35: Problem 10

What are the units of the wave function \(\psi(x)\) in a one-dimensional situation?

Short Answer

Expert verified
The units of the wave function \(\psi(x)\) in a one-dimensional situation are L^(-1/2), or inverse square root of length.

Step by step solution

01

Identify The Requirements

The probability of locating a particle within the space it is bound is 1. For a particle bound in one dimension and described by its wave function \(\psi(x)\), the requirement that the total probability to find the particle anyplace along x-axis is unity may be written as: \( \int_{-\infty}^\infty |\psi(x)|^2 dx = 1 \)
02

Determine Integral Dimensions

In this situation, \(x\) is a length, and so \(dx\) has dimensions of length (L). Then, the dimensions of the integrand \(|\psi(x)|^2 dx\) are: dimensions of \(|\psi(x)|^2\) times L. Given the right hand side is dimensionless (1 has no dimension), this indicates that the dimensions of \(|\psi(x)|^2\) are 1/L.
03

Obtain Wave Function Dimensions

Since the square of the absolute value of the wave function \(|\psi(x)|^2\) has dimensions of 1/L (inverse length), the dimensions of the wave function \(\psi(x)\) must be 1/\(\sqrt{L}\) or L^(-1/2). This is because the square root of the dimensions of 1/L gives the dimensions of the original function.

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Most popular questions from this chapter

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