Consider the wave function for the free particle Ae^ikx equation (41.1) At what value of X is the particle most likely to be found (a) at X=0 (b) at small Nonzero values of X (c) at large values of X (d) any where along the X axis

Solution

As the wave function for a free moving particle is given by equation 41.1 chapter 41 Quantum Mechanics

 𝚿(X) =Ae^ikx

But we know that the probability of finding a free particle about the position X is given by the equation/formula

P(X) dx = | 𝚿|² dx

As we know that | 𝚿|² is known as probability density and it’s value is given by the equation

| 𝚿|² = 𝚿* 𝚿

And 𝚿* 𝚿 = Ae^-ikx × Ae^ikx

  So | 𝚿|² = A²

Result/Answer
As the probability density is independent of the value of X because X is arbitrary and as a result particle most likely to be found anywhere along the X axis so option (d) is correct