What is the Born probablility interpretation?
The modulus squared of the wavefunction is proportional to the probability density for the measurement of position.
How do you normalise a wavefunction? [red]
- Identify the normalisation constant and the non normalised wave function in the given expression
- Identify the variable in the differential and the limits of integration which corresponds to all space for the particle
- Reason Borns probability theorum
- Solve for C and sub back into the equation
Does the wavefunction have to be normalised to calculate probabilities? [red]
Yes
What is the first postulate of Quantum Mechanics?
“The state of a non-relativistic quantum particle at time t is described by a non-singular complex wavefunction, which can be normalised so that the square of its modulus is equal to the probablity density for the results of a position measurement.”
What does it mean for a wavefunction to be normalisable?
Phi and its first derivative tend to zero at +/- infinity
What is the significance of a wavefunction being continuous and non-singular?
- A continuous wavefunction avoids ambiguous probablilities at different positions
- A non-singular wavefunction ensures we obtain a non-infinite and non-zero normalisatino constant and avoids singularities in the wavefunction
How do we get around the fact we cannot normalise a free particle wavefunction over +/- infinity?
Confine our free particle and limit all space to a large (but finite) region L.
