The behavior of a single electron in the double-slit experiment can indeed appear puzzling and seemingly in violation of the conservation of energy. However, this apparent violation arises from the probabilistic nature of quantum mechanics rather than a true violation of energy conservation.
In the double-slit experiment, when a single electron is fired at a screen with two slits, it behaves as both a particle and a wave. The electron wave function describes the probability distribution of finding the electron at different locations on the screen. The wave nature of the electron allows it to interfere with itself, leading to the observed interference pattern on the screen.
At any given moment, the electron can be detected at a specific location on the screen, which corresponds to a measurement of its position. However, prior to the measurement, the electron's position is described by a wave function that encompasses a range of possible positions.
The apparent unpredictability of the electron's movement arises because the outcome of a specific measurement is inherently probabilistic. The wave function of the electron gives us information about the probabilities of finding the electron at different positions on the screen. When multiple electrons are fired, the interference pattern emerges due to the accumulation of these probabilities.
Regarding energy conservation, it is important to note that the energy of the electron is conserved throughout the experiment. The behavior of the electron may seem unpredictable on an individual basis, but when averaged over many measurements, the energy conservation principle holds true.
In summary, the apparent violation of energy conservation in the double-slit experiment is resolved by recognizing the probabilistic nature of quantum mechanics. While the movement of a single electron may be uncertain and not easily predictable, the overall statistical behavior conforms to the principles of energy conservation.