Final answer:
Measuring the energy of a particle does change its wave function if it is not an eigenfunction of the Hamiltonian. The wave function undergoes collapse to an eigenstate of the Hamiltonian, reflecting the measurement's result, which is consistent with quantum mechanics principles such as the Copenhagen interpretation and Heisenberg uncertainty.
Step-by-step explanation:
The student asks whether measuring the energy of a particle changes its wave function (psi) if psi is not an eigenfunction of the Hamiltonian. In quantum mechanics, the wave function represents a system's state and contains information about all possible states of the system. When we measure a physical quantity like energy, we subject the wave function to 'collapse' if it is not already an eigenfunction of the corresponding operator—in this case, the Hamiltonian which represents the total energy of the system. This means that before measurement, the wave function can be a superposition of many different states, each with a different probability.
According to the Copenhagen interpretation of quantum mechanics, a wave function undergoes a collapse upon measurement, forcing the system into one of the eigenstates of the observable being measured. This change is represented by a transition from the superposition of states to a single state corresponding to the measured energy value. Furthermore, the Heisenberg uncertainty principle tells us that certain pairs of physical properties, like position and momentum, cannot be measured precisely at the same time, showing the inherent probabilistic nature of quantum systems.
The process of measurement affects the system, as described by Heisenberg's uncertainty principle. In quantum mechanics, this interaction between the measurement and the system results in a loss of information about certain complementary properties. Hence, if psi isn't an eigenfunction of the Hamiltonian before measurement, it will change to become one afterwards, reflecting the observed energy.