Question

can Ψ(x) =x^3 be a wave function in quantum mechanics​

Answer 1

Answer:

The function Ψ(x) =x^3 is not a wavefunction in quantum mechanics​

Explanation:

A wavefunction($\ \psi \left(x\right)$) gives the state of a quantum particle

The properties of an acceptable wavefunction are;

• The wavefunction should be finite, that is its value do not diverge to infinity
• The wavefunction must be continuous, that  is its graph has no discontinuity points
• It should be single-valued
• Its first derivative should be continuous
• It must be square-integrable, that is     $\int _{-\infty }^{\infty }\psi \left(x\right)^{\ast }\psi \left(x\right)dx<\infty$

The given function is

$\ \psi \left(x\right)=x^{3}$

this function obeys all the properties except the last one, that is the given function is not square-integrable

$\int _{-\infty }^{\infty }\psi \left(x\right)^{\ast }\psi \left(x\right)dx=\int _{-\infty }^{\infty }x^{3} *x^{3} dx =\infty$

the value  of the integral is not less than infinity so the given function is not a wavefunction