This is a guide to using the book, dealing with the Chapters 13 and 14 : quantum mechanics. The main point of this page is to try to assist you in using the book more effectively, in particular to stimulate an active approach: try to answer the questions in the book; think about them; return to them, until you have some understanding. (Within a reason.) Of course, some may simply turn out to be too difficult, or unrelated to what we are covering; please use your best judgement – and/or communicate with me. For some general notes on how this page should be understood and used, as well as some general comments on the material in the book, please refer to the similar page, posted previously, related to the midterm preparation. (If in any doubt, please contact me.)
A word on terminology may be in order. Please note that quantum theory has practically nothing ‘mechanical’ about it; this word has been coined in the analogy with ‘mechanics,’ as a study of basics of motion, and refers to the fact that these are the basics of what microscopic objects are, and how they move and behave. (The better sounding term “quantum physics” is mostly used for a broad variety of more complex phenomena, which are described using the principles of quantum mechanics.)
There is a number of ways to introduce basic principles of quantum mechanics. The way they are motivated and discussed in the book differs from what we did in the class; very quickly though, these methods converge (it is exactly the same physics) and one stays with the benefit of a variety of approaches.
This chapter presents the idea of the dual nature of radiation and matter. Section 13.1 points out the depth of the impact the quantum theory has on human knowledge (including our perceptions of ‘reality’), and just how profound quantum principles are. Sections 13.2 and 13.3 discuss radiation, now looking at its quantum-mechanical aspects; photo-effect is explained first. This is a landmark phenomenon showing that light behaves as composed of particles, which are called photons, and which can only have specific energies (“quantized,” coming in “quanta”); clearly, we know that light behaves as a wave, too – all the interference and diffraction phenomena confirm this. This strange observation, the fact that light will behave as a collection of particle-like objects (photons) under some circumstances, but also as a wave under other, is stated in section 13.3. The next two sections discuss the shocking fact that the same puzzle goes for matter : particles (electrons, for example) undergo typical wave phenomena, which cannot be explained by resorting to a picture of particles being little balls or lumps of matter – while, as we well know, they do behave as particles, too. Finally, section 13.6 asserts the need for a statistical interpretation: we can only think in terms of probabilities, or possibilities – particles/radiation are thought of as waves of tendencies, that will either interfere with each other and thus show wave-like behavior (if circumstances call for this), or manifest themselves as energy concentrated in small regions of space, exhibiting typical particle-like behavior. Both of these patterns of behavior are intrinsic to microscopic objects, each of them being a distinct possibility; it is the interaction with the surrounding environment that will bring out either side of their nature. Mathematically, this is represented by a function that can be used to calculate probabilities; it goes under a number of names, and this section uses the name 'Psi field.' Altogether, please focus on understanding the main idea (it is a deep one).
Concept Check:
(1, 2), 3 (p.355), (4, 5);
"MAKING ESTIMATES" (p.358) :
read it (the answer is in the footnote); (6-9); 10, 11
(If you can absorb the numbers used in 1-3, and precise terms of 'types of energy,'
these can be useful for appreciating the idea – #3 in particular)
Summary of Ideas and Terms: always potentially useful, but much more so in this chapter !
Review Questions:
1-3, (4); 7, 9; 10, 11; 20, 21, 23;
[ Comment :
Most of the questions here focus on emphasizing the evidence for the dual
nature of radiation and matter : this is real, both light and
matter indeed behave sometimes as waves, sometimes as particles; this
capacity, latent ability for both patterns of behavior, is in their nature,
it is what they are.
This is what we should get here, details only serve to illuminate it and, again,
to point out that this is very real and that microscopic objects just
are not little 'balls' or lumps of matter; and radiation is not simply waves.
]
Conceptual Exercises:
1, 2 (don't laugh :), (3-6), (7, 8 – good, general questions),
(9-10, interesting!); (11-14); 17, (19-22), 25, 26;
33, 34;
Please at least read (and think about) all these (even the ones in parenthesis),
and at least these.
Critical Thinking Exercises: very useful.
Having established the wave-particle duality in the previous chapter, the book now bites into the principles of quantum mechanics. First, two sections are devoted to atomic structure and, in particular, atomic transitions; historically this was the first big shock of quantum mechanics, and this is how we introduced it in the class. (Coming right from the discussion of radiation in electromagnetism, and having already talked about the molecular and atomic model, this was only natural.) Then sections 14.3 and 14.4 describe the indeterminacy principle (with one of the two Heisenberg's uncertainty relations) and “quantum jumps” (the fact that there is a certain discontinuity in microscopic processes, discrete behavior referred to by the very word ‘quantum’). Section 14.5 describes the prospect of an unsettling (scary?), and extremely interesting, possibility that there may well also be a certain ‘wholeness’ (as termed by Bohm), or non-locality : distant particles that have been “entangled” (interacted in a specific way), may know a thing or two about each other – without exchanging any information that we know of. This runs right against some very basic premises of modern physics and is very difficult to make sense of. Please pay some attention to section 14.6; the statements raised by quantum mechanics are very real. Section 14.7 is useful in a similar sense, to emphasize the extent of change in our perceptions that modern physics brings.
Concept Check:
(1 p378), (2-4; again, a bit too much of detail, otherwise could be useful), (5-7),
(8-10);
[ Comment :
Most of these questions refer to somewhat detailed descriptions from the text.
Try to use them to check your awareness of the basic principles, ideas
and meaning of these strange phenomena; they go completely against
our everyday intuition. You do not have to know the details.
]
Review Questions:
(4, 5); 7, (8), 9, 10, 11, (12); 13 (and you don't even have to look at the figure!),
14, (15), (16 – but it is a good one); (18, 20); 26, 27;
Conceptual Exercises:
(1-3, good questions, if you know the terminology used), 4 (lab!);
7, (8), 13-14 (Special Relativity here !);
(20-22; very useful to think through); 31-32;