# Can you see the quantum world

## Big Bang 7, textbook

Advanced Quantum Mechanics 36 RG 7.2 G 7.2 Extension of Quantum Physics 89 Summary The transition from the quantum world to the classical physics of large objects still poses problems. There are various interpretations of how to deal with this problem. The classic is the Copenhagen interpretation, the modern version the decoherence interpretation. 36.2 Quantum marble and quantum roller coaster The tunnel effect You may not notice one of the most spectacular effects of quantum mechanics directly, but in a certain way you owe it your life. It's the tunnel effect! Imagine flicking a marble against a book (Fig. 36.10). You would certainly be very amazed if it doesn't bounce off as expected (a), but just slips through the book (b). But that is exactly what can actually happen with quanta and we then speak of the tunnel effect. But how can that be? Z What is the relationship between energy and time uncertainty? Read up in chap. 33.6, p. 62! What is the difference between wave function and probability density? Read up in chap. 33.5, p. 62! Up to what points can you roll the car if you start at A on the roller coaster (Fig. 36.9)? Explain with the help of the conservation of energy! How could it look like on a “quantum rollercoaster”? Use the answer to F3 to think about it! The sun's heat is created by nuclear fusion inside. What does it mean? Which four basic forces are there in the universe? How big are they in relative terms and how far do they go? L F3 W1 F4 W1 F5 S1 Fig. 36.9: What would happen on a quantum roller coaster? F6 W1 F7 W1 Fig. 36.10: (a) A normal marble ricochets off the book. (b) A “quantum marble”, for example an electron, can “tunnel through” such obstacles under certain conditions. Let us first simplify the matter from three to one dimension (Fig. 36.10 c). In order for the ball to get past the book, it would have to take the detour over the upper edge. To do this, however, it needs potential energy. In a somewhat abstract way, the book represents a potential threshold that the sphere cannot pass. Now let's look at an analogous example from the quantum realm. When a quantum runs against a potential threshold, most of the probability wave is reflected (Fig. 36.11). This corresponds to the marble bouncing off. Amazingly, however, a small part of the wave runs through the obstacle. What does that mean? That the quantum will get through the obstacle with a certain probability - just tunnel effect. For the same reason, it could happen every now and then that you start at A on a “quantum rollercoaster” and still get to D (F5). Can one say which attempt the quantum tunnels through an obstacle? No! One can only make statements such as: “With 10 attempts, the quantum will tunnel through the obstacle once on average.” In the quantum realm, as is well known, dice are rolled! Fig. 36.11: A quantum runs against a potential threshold (see also Fig. 36.10 c). Because you cannot assign a path to this due to the uncertainty, the probability density is | Ψ | 2 shown. The higher this is at a certain point, the more likely the particle will be found there during a measurement. Why can a “quantum marble” pass through a potential threshold, but a real marble cannot pass through a book? Because the tunnel effect is a direct consequence of the energy uncertainty (F3). The quantum can borrow the missing energy ∆ E for a short period of time ∆ t in order to get over the mountain of energy. Ultimately, however, it appears as if the quant had tunneled through the mountain. The energy blurring is just a tiny little effect. In the case of a quant, this can be sufficient for it to pass through an actually forbidden area. In comparison with the energy of everyday objects, however, the energy uncertainty is not even a drop in the ocean. For testing purposes only - property of the publisher öbv