# 1. Show that (x) = Asin(kx) satisfies the time-independent Schrödinger equation when E and V are independent of x?

##### 1 Answer

#### Answer

#### Answer:

#### Explanation

#### Explanation:

You have provided a time-independent wavefunction, where the wavefunction is only a function of some dimension

The time independent Schrödinger equation, assuming a single nonrelativistic particle is:

Of course this equation states that the time-independent wavefunction is an eigenfunction of the Hamiltonian corresponding to an eigenvalue equal to the energy.

We can write the TI-equation expanded as:

Since we are only dealing with a

Our question asks us to consider the case where

Since we have found that the energy associated with this wavefunction is constant and not dependent on position, we have shown the wavefunction

It may also be useful to see that

This makes sense, since energy

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