Another example of a wave is a sound wave, which is vibrations of air

Niels Bohr, the biggest proponent of the Copenhagen interpretation, would reportedly criticize questions like, “Is the electron actually a particle, or is it a wave?”. An even function is a function that satisfies, In contrast, an odd function is a function that satisfies, An example of even and odd functions is shown in Figure \(\PageIndex{7}\). Note that the particle has one value of position for any time \(t\). Two observations are noteworthy. The specific form of the wavefunction depends on the details of the physical system. Two answers exist: (1) when the observer is not looking (or the particle is not being otherwise detected), the particle is everywhere (\(x = -\infty, +\infty\)); and (2) when the observer is looking (the particle is being detected), the particle “jumps into” a particular position state (\(x,x + dx\)) with a probability given by. Wave function ψ(x,y,z,t) of a particle is the amplitude of matter wave associated with particle at position and time represented by (x,y,z) and t. Some properties of wave function ψ: ψ is a continuous function; ψ can be interpretated as the amplitude of the matter wave at …

Visit this interactive simulation to learn more about quantum wave interference. For example, the wave function spreads across space, and this means that the particle itself doesn’t have a fixed location until you measure it, at which point the wave function “collapses,” and you obtain a definite value. \end{align}\]. The wavefunction of the ball can be written as \(\Psi \, (x,t) = C(0 < x < L)\), where \(C\) is a constant, and \(\Psi \, (x,t) = 0\) otherwise. To illustrate this interpretation, consider the simple case of a particle that can occupy a small container either at \(x_1\) or \(x_2\) (Figure \(\PageIndex{5}\)). Expectation-value calculations are often simplified by exploiting the symmetry of wavefunctions. The outcomes of measurements in quantum mechanics depend on probabilities, and so scientists can’t make definitive statements about the outcome of any one specific statement in the same way as in classical mechanics.

Under the right conditions, the same interference pattern develops for matter particles, such as electrons. The wave function or wave packet so constructed is found to have essentially zero ampli-tude everywhere except for a single localized region in space, over a region of width 2∆x, i.e. The subject is so powerfully not intuitive that there isn’t really much hope of understanding why nature behaves the way it does at the quantum level. The radioactive decay is a random [probabilistic] process, and there is no way to predict when it will happen.