No, the expectation value of position or momentum for a particle described by a wave function does not correspond to the classical values of absolute position and momentum that one would imagine for a classical particle. In quantum mechanics, particles do not possess definite values for position and momentum until they are measured.
The wave function of a particle represents the probability amplitude for finding the particle at a particular position or with a particular momentum. The expectation value of a physical observable, such as position or momentum, is calculated by taking the average of all possible measurement outcomes weighted by the probabilities given by the wave function.
For example, the expectation value of position (x) is given by the integral of the position multiplied by the probability density function (|ψ(x)|^2) over all possible positions:
⟨x⟩ = ∫ x |ψ(x)|^2 dx
Similarly, the expectation value of momentum (p) is given by the integral of the momentum operator (p̂) acting on the wave function, multiplied by the complex conjugate of the wave function, integrated over all possible momenta:
⟨p⟩ = ∫ ψ*(x) p̂ ψ(x) dx
These expectation values represent the average values that would be obtained from repeated measurements on an ensemble of identically prepared quantum systems.
It's important to note that due to the inherent probabilistic nature of quantum mechanics, the expectation values may not correspond to any specific classical value. Quantum particles can exhibit wave-like behavior and can be in superposition states where they can be simultaneously spread out over multiple positions or momenta until they are measured and "collapse" to a specific value.