Question

cannol-
Q. Which of the following
wave functions can not be
solution of Schrodinger equation for all values of x?
a) Y=Asec(x)
b) Y = A tan (x)
c) Y=Ae^-x²
d) Y = A ex²
​

Answer 1

Answer:

Option b

hope its correct

Answer 2

Given,

a) Y = Asec(x)

b) Y = Atan(x)

c) Y = $Ae^{-x^{2} }$

d) Y = $Ae^{x^{2} }$

To Find,

Which of the following wave functions can not be solution of Schrodinger equation for all values of x?

Solution,

We know that,

The temporal and spatial evolution of a quantum mechanical particle is described by a wave function Y(x,t) for 1-D motion Y(r,t) for 3-D motion. It contains configuration space wave functions.

Contitions for a physically accepted, well-behaved and realistic wave functions are as follows:

(i) Y(x,t) should be finite, single-valued and continuous everywhere in space.

(ii) dY/dx should be continuous everywhere in space.

(iii) Y(x,t) should be square-integrable.

Now, according to this

a) Asec(x) is not finite at π/2

b) Atan(x) is not finite at π/2

c) Y = $Ae^{-x^{2} }$ is finite everywhere in space and continuous too

d) Y = $Ae^{x^{2} }$ is not finite at x = ±∞

Hence, a)Y = Asec(x), b)Y = Atan(x) and d) Y = $Ae^{x^{2} }$  cannot be

solution of Schrodinger equation for all values of x.