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Section 24.3: The Heisenberg Uncertainty Principle

Exercise 35

Step 1

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Since the uncertainty principle states that

$$
Delta pDelta xgeqfrac{h}{2pi}
$$
we see that

$$
Delta pgeqfrac{frac{h}{2pi}}{Delta x}.
$$
so if we decrease $Delta x$ we divide by smaller number and thus increase $Delta p$ i.e. increase uncertainty in the momentum.

Result

2 of 2

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Exercise 36

Step 1

1 of 2

Since the uncertainty principle states that

$$
Delta EDelta tgeqfrac{h}{2pi}
$$
we see that

$$
Delta Egeqfrac{frac{h}{2pi}}{Delta t}.
$$
so if we increase $Delta t$ we divide by greater number and thus decrease $Delta E$ i.e. uncertainty in the energy.

Result

2 of 2

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Exercise 37

Step 1

1 of 2

They call it the tunnel effect. This is a name for an observed effect of a particle moving through regions that are classically forbidden in a sense that particle classically wouldn’t have enough energy to reach them.

Result

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Exercise 38

Step 1

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We expect tunneling current to increase. The current drops as the potential barrier created by the gap increases because the electrons are less likely to tunnel. If we decrease the gap more of them will tunnel and the current would increase.

Result

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Section 24.3: The Heisenberg Uncertainty Principle

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