Since quantum mechanics, special theory of relativity, and all other theories are still only theories
I agree with what you wrote with the exception of Quantum Mechanics.
Quantum mechanics is used in actual applications in the real world.
Theories are not.
Many modern electronic devices are designed using quantum mechanics. Examples include the laser, the transistor (and thus the microchip), the electron microscope, and magnetic resonance imaging (MRI).'
Researchers are currently seeking robust methods of directly manipulating quantum states.
Quantum is no longer a theory.
Solvable systems
The two-state quantum system (the simplest quantum system that can exist)
The free particle
The delta potential
The Double well Dirac delta potential
The particle in a box / infinite potential well
The finite potential well
The One-dimensional triangular potential
The particle in a ring or ring wave guide
The particle in a spherically symmetric potential
The quantum harmonic oscillator
The quantum harmonic oscillator with an applied linear field
The hydrogen atom or hydrogen-like atom e.g. positronium
The hydrogen atom in a spherical cavity with Dirichlet boundary conditions
The Hydrogen Molecular ion (Solutions in terms of generalized Lambert W function)
The particle in a one-dimensional lattice (periodic potential)
The Morse potential
The step potential
The linear rigid rotor
The symmetric top
The Hooke's atom
The Spherium atom
Zero range interaction in a harmonic trap
The Quantum pendulum
The Rectangular potential barrier
The Pöschl-Teller potential
The Inverse square root potential
The Lambert-W step-potential
Multistate Landau–Zener Models
~ wiki
Theories do not have solvable systems.
Many people think that human science is highly advanced but I liken it to the knowledge of a 2 year old. There is still 'oh so much' to learn.