我來亂侃幾句。首先聲明一下，我非常崇拜和敬仰 Weinberg 教授的才華和對科學的貢獻。我提出的問題純粹針對學術討論。



在書中 [Steven Weinberg, Lectures on Quantum Mechanics, (Cambridge, New York, 2013), p. 61], Weinberg 教授說:

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3.3 Observables

According to the second postulate of quantum mechanics, observable physical quantities like position, momentum, energy, etc., are represented as Hermitian operators on Hilbert space. An Hermitian operator is one that is linear and self adjoint. So before we spell out what this postulate means, we need to consider what is meant by operators in general, by linear operators in particular, and by the adjoint of an operator.

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“An Hermitian operator is one that is linear and self adjoint.”  這句話意味着厄米特算符（Hermitian operator ）是自伴算符（self adjoint）。這個說法對於無限維函數空間好象不成立，受到數學家們的質疑。他們說自伴算符是厄米特算符，但厄米特算符未必是自伴算符。只有自伴算符才能正確描述可測物理量（observable），而不是厄米特算符。