This analysis reveals common errors in expectations and localization of a quantum particle in a box, highlighting implications for understanding quantum mechanics.
The most basic example of a quantum mechanical problem, the one-dimensional particle in a box, is revisited. Three aspects are treated. 1.It is shown that a number of textbooks give an incorrect result for the expectation value of x2, and, therefore, do not obtain the correct spread Δx. Consequently, the verification of the Heisenberg relation is also in error. 2. It is found that textbooks do not mention the origin dependence of expectation values, which is a nuisance, as the problem is evidently treated in the literature with two choices of origin. 3. Superposition of an infinite number of even (cosine) solutions of the one-dimensional particle in the box allows for an analytical demonstration of complete localization of the particle (Δx = 0).
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J. J. C. Mulder (2002) studied this question.
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