Not added. One must form the "tensor product" of the two Hilbert spaces.ashutoshsharma said:the wave functions of individual particles can be added together to create a wave function for for system,
tom.stoer said:Consider a single particle wave function ψ(x) for a single particle. Adding two such wave functions ψa(x) + ψb(x) still describes one single particle.
In order to describe two particles you have to introduce two positions x and y and you have to use the product ψa(x) * ψb(y)
The addition of wave functions for a system is important because it allows us to combine the different possible states of a system and determine the overall probability of finding the system in a certain state. This is a fundamental aspect of quantum mechanics and helps us understand the behavior of particles at the microscopic level.
Yes, the wave functions of two or more systems can be added together as long as they are in the same quantum state. This is known as superposition and is a key concept in quantum mechanics.
When two wave functions with opposite phases are added together, they cancel each other out and result in a wave function with a smaller amplitude. This is known as destructive interference and can occur when two particles are in opposite locations and their wave functions overlap.
The total probability of finding a system in a certain state is calculated by squaring the sum of the individual wave functions. This takes into account the amplitudes and phases of each wave function and gives us the overall probability of finding the system in that state.
While the addition of wave functions is most commonly used in quantum mechanics, it can also be applied to classical systems. However, in classical systems, the wave functions represent probabilities rather than physical states, as in quantum mechanics.