|Mar29-08, 08:35 AM||#1|
Quantum mechanics - a free particle
If we measure the position of a particle in a free space, and say we find that it is at x0,
what is the wavefunction right after the measurement in x representation?
shouldn't it be delta (x-x0), because delta functions are the eigenfunctions of the position operator?
Another question is how do I find the eigenfunctions of the Hamiltonian of a free particle in x representation?
Thanks in advance
|Mar29-08, 09:00 AM||#2|
|Apr10-08, 12:29 PM||#3|
I solved the Schrodinger equation and got the function:
This means that any private case (like A=0 and B=1) is an eigenfunction of the Hamiltonian. Can I conclude that the Hamiltonian has an infinite number of eigenfunctions?
I also notice that there are only two basic "types" here - exp(ikx) and exp(-ikx).
Does it mean that these two form a basis of the Hamiltonian eigenfunctions space? is it considered as a Hilbert space?
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