6- The Schrödinger Equation

Question 1

TDSE

Answer 1

Question 2

TISE

(Energy = 0)

Answer 2

Question 3

TISE

Answer 3

Question 4

Schrödinger equation governs the propagation of….

Answer 4

matter waves

Question 5

Schrödinger equation cannot be derived in much of the same way Newstons laws of motion cant be derived. Its validity, like that of any fundamental equation, lies in…

Answer 5

its agreement with experimental data.

Question 6

Like Newtons laws of motion are not relativistically correct…

Answer 6

neither is Schrödingers equation, which must ultimately yield to a relativistic wave equation.

Question 7

Diract, in 1928….

Answer 7

successfully developed a relativistic Schrödinger equation.

Question 8

If Ψ1(x,t) and Ψ2(x,t) are both solutions of the wave equation for the same potential energy, then…

Answer 8

any linear combination of te two solutions is also a solution.

Linearity guarantees that the wave functions wil add together to produce constructive and destructive interference.

Question 9

Linearity requirement means that every term in the wave equation must be linear in Ψ(x,t) and…

Answer 9

any derivative of Ψ(x,t) is linear in Ψ(x,t).

Question 10

An important difference between the Schrodinger equation and the classical wave equation is…

Answer 10

the explicit appearance of the imaginary number, i. The wave functions that satisfy the Schrodinger equation are not necessarily real.

Question 11

The aspect that we can “measure” in a solution to a Schrodinger equation is…

Answer 11

the probability that the electron will be found in a differential unit of volume.

Question 12

The probability othat an electron will be found in the volume dx is equal to …

Answer 12

Developed by Max Born.

Ψ²dx

We can run many trials and measure the density of the electron positions (fraction of time it spends in each region, dx)