Number of Nodes in energy eigenstates

The physical interpretation behind the increase of energy with the number of nodes can be understood in a very crude manner as follows:

Nodes are points of zero probability densities. Since the wavefunction is continuous, the probability density is also a continuous function. So the regions in the neighbourhood of nodes will have small probability densities. Physically, this means that the particle has less space to move around. That is, the particle is more confined and uncertainty in position $(\Delta x)$ decreases. This increases $\Delta p$ (due to the uncertainty principle), causing an increase in energy. Hence, the energy increases as the number of nodes increase. So the ground state should not have any node.