By Robert B. Griffiths
This quantity elucidates the constant quantum thought method of quantum mechanics at a degree obtainable to college scholars in physics, chemistry, arithmetic, and computing device technology, making this an incredible complement to plain textbooks. Griffiths offers a transparent rationalization of issues no longer but properly taken care of in conventional texts and which scholars locate complicated, as do their lecturers. The e-book can also be of curiosity to physicists and philosophers engaged on the principles of quantum mechanics.
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Extra resources for Consistent Quantum Theory
3) is zero. As discussed in Sec. 3, if a wave function vanishes outside some finite interval, the quantum particle is located inside that interval. Since the two intervals [x1 , x2 ] and [x3 , x4 ] in Fig. 3 do not overlap, they represent mutuallyexclusive possibilities: if the particle is in one interval, it cannot be in the other. In Fig. 4, ψ(x) and φ(x) are the ground state and first excited state of a quantum particle in a smooth, symmetrical potential well (such as a harmonic oscillator).
23). The inverse transformation is 1 ψ(m) = √ M ˆ e2πikm/M ψ(k). 24), can equally well be written in terms of momentum wave functions: ˆ φˆ ∗ (k)ψ(k). 17). The main difference is that integrals have been replaced by sums. The reason h¯ has disappeared from 26 Wave functions the toy model expressions is that position and momentum are being expressed in dimensionless units. 1 Hilbert space and inner product In Ch. 2 it was noted that quantum wave functions form a linear space in the sense that multiplying a function by a complex number or adding two wave functions together produces another wave function.
Whether or not “cutting off the tails” in this manner is an acceptable approximation is a matter of judgment, just as in the case of the position wave packet discussed in Sec. 3. 14). 21). 19) with p0 = 0 and p = h¯ /2 x. 21). Probabilities will be taken up later in the book, but for present purposes it suffices to regard x and p as convenient, ˆ p), albeit somewhat crude measures of the widths of the wave packets ψ(x) and ψ( respectively. What the inequality tells us is that the narrower the position wave ˆ p) has got packet ψ(x), the broader the corresponding momentum wave packet ψ( to be, and vice versa.