Proper Wavefunctions ( ψ ) in Quantum Mechanics Must Be $\int_{-\infty}^{\infty}[\psi(x)]^{2} d x=1$

question 15

Multiple Choice

Proper wavefunctions ( ψ ) in quantum mechanics must be normalized. Which statement below best summarizes this mathematically?

• A) \(\int_{-\infty}^{\infty}[\psi(x)]^{2} d x=1\)
• B) \(\int_{-\infty}^{\infty} \psi(x) d x=1\)
• C) \(\int_{-\infty}^{\infty}[\psi(x)]^{2} d x=0\)
• D) \(\lim _{x \rightarrow \infty}\) \(\psi(x)=0\)
• E) \(\psi(x)=\sin \left(\frac{n \pi x}{L}\right) ; n=1,2,3 \ldots\)

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Definitions:

Expected Return

The weighted average of all possible returns, with weights equal to the probabilities of each outcome.

Equally-Weighted

An investment strategy where each security is assigned the same weight or importance in a portfolio, promoting diversification.

Risk-Free Asset

An investment with a certain return, usually with low returns, considered to have negligible risk, such as government bonds.

Expected Return

The anticipated value or profit gained from an investment over a specified period, considering all possible outcomes.