Quantum Mechanics by Wan K. Kong;

Author:Wan, K. Kong;
Language: eng
Format: epub
Publisher: Jenny Stanford Publishing
Published: 2021-09-15T00:00:00+00:00

(2) Since corresponds to a constant function of value for all x ∈ Ʌ a formal differentiation of this constant function lead to the zero function which would corresponds to the zero vector in , i.e., we will get (∗∗∗∗)

This would imply

This cannot be correct since Eq. (∗∗∗∗) above implies that is an eigenvector of corresponding to an eigenvalue 0. But Eq. (19.44) tells us that does not have a zero eigenvalue. Another way of looking at this is to realise that

cannot be smaller than the smallest eigenvalue of given by Eq. (19.44). This is because

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