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koustav
- 29
- 4
Thread moved from the technical forums and poster has been reminded to show their work
Summary:: I am trying to find the exact ground state energy of the hamiltonian.kindly help me with this
there will be vector sign and no square on the last termHaborix said:To the OP, would you clarify the typo in the last term, just so we are all certain what we're working with.
The 3D harmonic oscillator is a physical system that follows the laws of quantum mechanics and can be described by a mathematical model called the harmonic oscillator potential. It is a three-dimensional version of the simple harmonic oscillator, which is a system that oscillates back and forth around a stable equilibrium point.
The ground state energy of a 3D harmonic oscillator is the lowest possible energy that the system can have. In other words, it is the energy of the system when it is in its most stable state, with no additional energy added to it.
The ground state energy of a 3D harmonic oscillator can be calculated using the Schrödinger equation, which is a fundamental equation in quantum mechanics. This equation takes into account the potential energy of the system and the mass of the particle, and it allows us to determine the energy levels of the system.
The ground state energy of a 3D harmonic oscillator is significant because it is the starting point for calculating the energy levels of the system. It also represents the lowest possible energy that the system can have, and it is used as a reference point for comparing the energy of the system in its excited states.
The 3D harmonic oscillator is a simplified model that can be used to describe various physical systems, such as atoms, molecules, and even macroscopic objects like springs. The ground state energy of a 3D harmonic oscillator is a fundamental concept in quantum mechanics and can help us understand the behavior of these systems in their most stable state.