Are the following statements true or false, and clearly explain why you arrived

ID: 3162737 • Letter: A

Question

Are the following statements true or false, and clearly explain why you arrived at that conclusion.

1. Any momentum operator or linear combinatior of momentum operators will always commute with the Hamiltonian operator.

2. The kinetic energy of a quantum mechanical particle can always be determined to arbitrary precision.

3. For a particle-in-a-box, any state that is a linear combination of multiple eigenstates will have a time-dependent average position.

4. Different eigenstates of any Hamiltonian are always orthogonal to each other.

1) Hamiltonin operator gives the value of energy. It is equal to the sum of kinetic and potential energies.

The kinetic energy has a term of momentum square but not the momentum.

So momentum will not commute with Hamiltonian where as square of the momentum commute.

So the given statement is false.

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.