In [[Quantum Mechanics|quantum mechanics]], there are systems where certain quantities can only take [[Discreteness|discrete values]]. One example for such a quantity is the [[Energy|energy]]. To understand how weird that is, let us have a look at some physical objects from our everyday life. If we accelerate in a car, we do not expect the speedometer to jump from $10\,\text{km}/\text{h}$ directly to $20\,\text{km}/\text{h}$. While pushing down the pedal, the needle will smoothly move between the two. The same goes for a thermometer in a pot of water. If we place the pot on a stove, the thermometer (think about a mercury thermometer) will smoothly rise and show all temperatures up to the point of boiling. In both systems, we increase their [[Energy|energy]]. In the case of the car, its kinetic energy, in the second case we enlarge the thermal energy of the water. In [[Quantum Mechanics|quantum mechanics]], there are systems where an imaginary thermometer or speedometer will not move smoothly. Only certain energies are allowed. ![[energy_levels.excalidraw.light.svg]] The energy spectrum on the right shows an example of [[Discreteness|discrete]] energy levels. The lowest two levels, marked in red, could be used to [[Implementation|implement]] a [[Qubit|qubit]]. >[!read]- Further Reading >- [[Discreteness]] >- [[Quantum Mechanics]] >[!ref]- References