Final answer:
The integral from negative to positive infinity of the squared wave function equals one signifies a normalization condition in quantum mechanics, ensuring the total probability of finding a particle anywhere in space is 100%.
Step-by-step explanation:
The expression ∞ +| |2 dx = 1 represents a normalization condition in quantum mechanics where the integral of the square of the wave function, |Y(x,t)|2, over the entire space must equal to one. This establishes that the probability of finding a particle somewhere in space is 100%. The wave function itself, Y(x,t), contains information about the quantum state of a particle, with its magnitude squared, |Y(x,t)|2, providing the probability density of locating the particle at position x at time t, as per the Born interpretation. When the wave function is integrated over a range, such as from negative to positive infinity, you get the probability volume, which for a normalized wave function this probability must sum to one indicating certainty that the particle exists somewhere within the defined space.