Simple Nature - Light and Matter

c/Energy levels of the N 2 molecule. d/Excited states of the nu- cleus^178 Hf. Black squares represent states that are inter- pr ...

Note that only even multiples of~are observed in collective rotation in figure d. This is because the nucleus’s shape has an add ...

librium position, so ∆x= 0. But this would violate the Heisenberg uncertainty principle and so is impossible. The inevitable mot ...

the wavefunction Ψ 10 shown in figure d on p. 923, for`= 1 and `z= 0. (The odd value of`is possible for a rotor that doesn’t hav ...

For vectors in three-dimensional space, a set of three vectors is not linearly independent if they lie in the same plane. The se ...

Unobservability of phase and normalization When we say that phase and normalization don’t count as knowledge of a system, we’re ...

wave along a deterministic trajectory. Another example that shows the contrast with the classical de- scription is that if I sho ...

and if this is to hold true for all values ofxandt, then we must have~ω=~ (^2) k 2 2 m, which is simply an expression of the New ...

Linear algebra application Time evolution is represented by a linear operator (p. 965). Unitarity is an additional re- quirement ...

two states, one in which the atom has decayed and your brain has observed that fact, and one in which the atom has not yet decay ...

a/An incident wave is partially reflected and partially transmitted at a step in the potentialU. The complex wavefunctions are r ...

b/A particle in a box. One of our principles of quantum mechanics is unitarity (p. 969), which says, in part, that probability i ...

figure b/2, where√ kis a positive real number satisfyingk=p/~= 2 mE/~. Ψ 1 is a wave traveling to the right, and Ψ 2 is a wave t ...

c/A solution to the Schrodinger ̈ equation found by separability. Positive values are shown as light colors, negative ones as da ...

tion. The output shouldn’t depend on amplitude (because a dif- ferent amplitude might just mean an incorrectly normalized state ...

Linear algebra application Observables are represented a linear operators (p. 965). We also require that this operator have real ...

momentum is a sine wave of the formΨ=ei k x. We havekλ= 2π andp=h/λ=~k, and the sign is a matter of convention. Taking the deriv ...

Its graph is an infinitely narrow, infinitely tall spike atx= 0, and it has ∫+∞ −∞δ(x) dx= 1. Mathematicians will shake their he ...

By way of rigorous proof, suppose to the contrary that we did have such an observableOph. By our definition of an observ- able, ...

Since you’ve already studied relativity, you’ve had carefully in- culcated in you the idea that space and time are to be treated ...