我来乱侃几句。首先声明一下，我非常崇拜和敬仰 Weinberg 教授的才华和对科学的贡献。我提出的问题纯粹针对学术讨论。



在书中 [Steven Weinberg, Lectures on Quantum Mechanics, (Cambridge, New York, 2013), p. 61], Weinberg 教授说:

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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.”  这句话意味着厄米特算符（Hermitian operator ）是自伴算符（self adjoint）。这个说法对于无限维函数空间好象不成立，受到数学家们的质疑。他们说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确描述可测物理量（observable），而不是厄米特算符。