## 1.1) The Schrodinger Equation

For conservative systems, force can be expressed as a derivative of potential energy function. So, $F=\frac{-\partial V}{ \partial x}$.

While classical mechanics determines the position of any object at time t through newton’s laws, force and momentum concepts, Quantum mechanics defines $(x,t)$ as wavefunction $\psi$ and it solved with the help of Schrodinger’s Equation:

$$i\hbar\frac{\partial\psi}{\partial t}=-\frac{\hbar^{2}}{2m}\frac{\partial^{2}\psi}{\partial x^{2}} + V\psi$$

Active quaraple sys

Here $i$ is imaginary number and $\hbar$ is Plank’s Constant divided by $2\pi$:

$$\hbar=\frac{h}{2r}=1.054\times10^-34 \text{ }Js$$

## 1.2) Statistical Interpretation

Wavefunction is more useful in certain cases due to Born’s Statistical Interpretation which states that $|\psi (x,t)^{2}|$ gives the probability of finding particle at $x$ at time $t$.

$\int_{a}^{b} |\psi (x,t)^{2}| \text{ } dx =$ $\text {Probablity of finding particle between a and b at time t.}$ Probability is area under the graph of $|\psi^{2}|$. This equation introduces indeterminacy in quantum mechanics.

Current theory relies on an Orthodox Position meaning that observation disturb what they measure and essentially a it is the measurement process which insists on a definite value while creating results.