Problem 5-13 Discuss the possibility of interpreting $\phi_n(x)$ as a $\chi_{a, b, c, \dotsb}(x)$ function discussed in Sec. 5-2. That is, say $\phi^{*}_n(x)$ is the transformation function to go from the $x$ representation to a representa…

Problem 5-12 Show that the $x$ coordinate of position and the $x$ coordinate of momentum are not simultaneously measurable quantities. ( 解答 ) 問題 5-9 と問題 5-10 とから, 運動量の $x$ 成分に対する演算子は $\displaystyle{\hat{p}_x=\frac{\…

Problem 5-11 The wave function $\chi_{a,b, c, \dotsb}(x)$, as discussed in Sec. 5-2, shows a particularly simple behavior when subjected to the operator $\mathcal{A}$. Thus $ \def\bra#1{\langle#1|} \def\BK#1#2{\langle #1|#2\rangle} \def\Br…

Problem 5-10 Suppose the quantity $A$ corresponds to the $x$ coordinate of position. Show that the correct formula for the expected value of $x$ results when the function $G_A(x,x^{'})$ is taken to be $ \def\bra#1{\langle#1|} \def\BK#1#2{\…

Problem 5-9 The transformation function between space representation and momentum representation is $ \def\bra#1{\langle#1|} \def\BK#1#2{\langle #1|#2\rangle} \def\BraKet#1#2#3{\langle#1|#2|#3\rangle} \def\ppdiff#1#2{\frac{\partial #1}{\pa…