p40_018 - m 2 / s 2 , then we see the above is indeed in...

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18. (a) We recall that a derivative with respect to a dimensional quantity carries the (reciprocal) units of that quantity. Thus, the Frst term in Eq. 40-18 has dimensions of ψ multiplied by dimensions of x 2 . The second term contains no derivatives, does contain ψ , and involves several other factors that (as we show below) turn out to have dimensions of x 2 : 8 π 2 m h 2 [ E U ( x )] = kg (J · s) 2 [J] assuming SI units. Recalling from Eq. 7-9 that J = kg
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Unformatted text preview: m 2 / s 2 , then we see the above is indeed in units of m 2 (which means dimensions of x 2 ). (b) In one-dimensional Quantum Physics, the wavefunction has units of m 1 / 2 as Sample Problem 40-2 shows. Thus, since each term in Eq. 40-18 has units of multiplied by units of x 2 , then those units are m 1 / 2 m 2 = m 2 . 5 ....
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