bekjunhao said:Homework Statement
Given state: |ψ> = |0> + α|1> + σ^2/√2 |2>
find the wavefunctions.
I am confused between states and wavefunctions, everywhere I've read it says that state (ie the wavefuctions), really need some enlightenment here..
bekjunhao said:So i understand for the second state there wouldn be any wavefunctions as it is a mixed state.
The first state however is a pure state, so i went like x|ψ> . But after that I am stuck, any hints so that i can continue?
bekjunhao said:Eh I think it's confusing with the notations used in the question.. But it isint the density matrix... Just a mixed state
A wavefunction, also known as a quantum state, is a mathematical function that describes the quantum state of a particle or system. It contains information about the probability of finding the particle in a particular state, as well as other physical properties. In quantum mechanics, the wavefunction is crucial in understanding the behavior of particles at the microscopic level.
To find the wavefunction, you need to solve the Schrödinger equation, which is a differential equation that describes the evolution of a quantum system. The solution to this equation is the wavefunction, which can be found by using mathematical techniques such as separation of variables, perturbation theory, or numerical methods.
There are two main types of states that can be used to find the wavefunction: eigenstates and superposition states. Eigenstates are stationary states with definite energy levels, while superposition states are a combination of multiple eigenstates with different energies. By using a linear combination of eigenstates, any wavefunction can be constructed.
No, the wavefunction itself cannot be measured or directly observed. It is a mathematical construct that describes the quantum state of a particle or system. However, the properties and behavior of the particle can be observed and measured based on the information contained in the wavefunction.
One limitation is that the Schrödinger equation can only be solved analytically for simple systems with known potentials. For more complex systems, numerical methods must be used, which can be computationally demanding. Additionally, the wavefunction only describes the behavior of a single particle or system, and cannot account for interactions with other particles or external factors.