Energy Eigen Values for 3D SHO Calculator

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✖Energy Levels of 3D Oscillator along X axis are the quantised energy levels in which a particle may be present.ⓘ Energy Levels of 3D Oscillator along X axis [n_x]			+10% -10%
✖Energy Levels of 3D Oscillator along Y axis are the quantised energy levels in which a particle may be present.ⓘ Energy Levels of 3D Oscillator along Y axis [n_y]			+10% -10%
✖Energy Levels of 3D Oscillator along Z axis are the quantised energy levels in which a particle may be present.ⓘ Energy Levels of 3D Oscillator along Z axis [n_z]			+10% -10%
✖Angular Frequency of Oscillator is the angular displacement of any element of the wave per unit of time or the rate of change of the phase of the waveform.ⓘ Angular Frequency of Oscillator [ω]			+10% -10%

✖Energy Eigen Values of 3D SHO is the energy possessed by a particle residing in the nx, ny and nz energy levels.ⓘ Energy Eigen Values for 3D SHO [E_(nx,ny,nz)]

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Energy Eigen Values for 3D SHO

Formula

`"E"_{"(nx,ny,nz) "} = ("n"_{"x"}+"n"_{"y"}+"n"_{"z"}+1.5)*"[h-]"*"ω"`

Example

`"1.3E^-33J"=("2"+"2"+"2"+1.5)*"[h-]"*"1.666rad/s"`

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Energy Eigen Values for 3D SHO Solution

STEP 0: Pre-Calculation Summary

Formula Used

Energy Eigen Values of 3D SHO = (Energy Levels of 3D Oscillator along X axis+Energy Levels of 3D Oscillator along Y axis+Energy Levels of 3D Oscillator along Z axis+1.5)*[h-]*Angular Frequency of Oscillator
E_(nx,ny,nz) = (n_x+n_y+n_z+1.5)*[h-]*ω
This formula uses 1 Constants, 5 Variables

Constants Used

[h-] - Reduced Planck constant Value Taken As 1.054571817E-34

Variables Used

Energy Eigen Values of 3D SHO - (Measured in Joule) - Energy Eigen Values of 3D SHO is the energy possessed by a particle residing in the nx, ny and nz energy levels.
Energy Levels of 3D Oscillator along X axis - Energy Levels of 3D Oscillator along X axis are the quantised energy levels in which a particle may be present.
Energy Levels of 3D Oscillator along Y axis - Energy Levels of 3D Oscillator along Y axis are the quantised energy levels in which a particle may be present.
Energy Levels of 3D Oscillator along Z axis - Energy Levels of 3D Oscillator along Z axis are the quantised energy levels in which a particle may be present.
Angular Frequency of Oscillator - (Measured in Radian per Second) - Angular Frequency of Oscillator is the angular displacement of any element of the wave per unit of time or the rate of change of the phase of the waveform.

STEP 1: Convert Input(s) to Base Unit

Energy Levels of 3D Oscillator along X axis: 2 --> No Conversion Required
Energy Levels of 3D Oscillator along Y axis: 2 --> No Conversion Required
Energy Levels of 3D Oscillator along Z axis: 2 --> No Conversion Required
Angular Frequency of Oscillator: 1.666 Radian per Second --> 1.666 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_(nx,ny,nz) = (n_x+n_y+n_z+1.5)*[h-]*ω --> (2+2+2+1.5)*[h-]*1.666

Evaluating ... ...

E_(nx,ny,nz) = 1.31768746427382E-33

STEP 3: Convert Result to Output's Unit

1.31768746427382E-33 Joule --> No Conversion Required

FINAL ANSWER

1.31768746427382E-33 ≈ 1.3E-33 Joule <-- Energy Eigen Values of 3D SHO

(Calculation completed in 00.004 seconds)

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Created by Ritacheta Sen

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Energy Eigen Values for 3D SHO

Go Energy Eigen Values of 3D SHO = (Energy Levels of 3D Oscillator along X axis+Energy Levels of 3D Oscillator along Y axis+Energy Levels of 3D Oscillator along Z axis+1.5)*[h-]*Angular Frequency of Oscillator

Energy Eigen Values for 2D SHO

Go Energy Eigen Values of 2D SHO = (Energy Levels of 2D Oscillator along X axis+Energy Levels of 2D Oscillator along Y axis+1)*[h-]*Angular Frequency of Oscillator

Energy Eigen Values for 1D SHO

Go Energy Eigen Values of 1D SHO = (Energy Levels of 1D Oscillator+0.5)*([h-])*(Angular Frequency of Oscillator)

Restoring Force of Diatomic Vibrating Molecule

Go Restoring Force of Vibrating Diatomic Molecule = -(Force Constant of Vibrating Molecule*Displacement of Vibrating Atoms)

Potential Energy of Vibrating Atom

Go Potential Energy of Vibrating Atom = 0.5*(Force Constant of Vibrating Molecule*(Displacement of Vibrating Atoms)^2)

Zero Point Energy of Particle in 2D SHO

Go Zero Point Energy of Particle in 2D SHO = [h-]*Angular Frequency of Oscillator

Zero Point Energy of Particle in 1D SHO

Go Zero Point Energy of 1D SHO = 0.5*[h-]*Angular Frequency of Oscillator

Zero Point Energy of Particle in 3D SHO

Go Zero Point Energy of 3D SHO = 1.5*[h-]*Angular Frequency of Oscillator

Energy Eigen Values for 3D SHO Formula

What happens in case of accidental degeneracy ?

In quantum mechanics, accidental degeneracy refers to energy degeneracy that occurs coincidentally, without any protection by symmetry. Generally, an accidental degeneracy occurs due to accidental symmetries that can lead to additional degeneracies in the discrete energy spectrum. As an example of accidental degeneracy, we can consider a particle in a constant magnetic field.

How to Calculate Energy Eigen Values for 3D SHO?

Energy Eigen Values for 3D SHO calculator uses Energy Eigen Values of 3D SHO = (Energy Levels of 3D Oscillator along X axis+Energy Levels of 3D Oscillator along Y axis+Energy Levels of 3D Oscillator along Z axis+1.5)*[h-]*Angular Frequency of Oscillator to calculate the Energy Eigen Values of 3D SHO, The Energy Eigen Values for 3D SHO formula is defined as the energy that a particle possess residing in that quantised energy level. Energy Eigen Values of 3D SHO is denoted by E_(nx,ny,nz) symbol.

How to calculate Energy Eigen Values for 3D SHO using this online calculator? To use this online calculator for Energy Eigen Values for 3D SHO, enter Energy Levels of 3D Oscillator along X axis (n_x), Energy Levels of 3D Oscillator along Y axis (n_y), Energy Levels of 3D Oscillator along Z axis (n_z) & Angular Frequency of Oscillator (ω) and hit the calculate button. Here is how the Energy Eigen Values for 3D SHO calculation can be explained with given input values -> 1.3E-33 = (2+2+2+1.5)*[h-]*1.666.

FAQ

What is Energy Eigen Values for 3D SHO?

The Energy Eigen Values for 3D SHO formula is defined as the energy that a particle possess residing in that quantised energy level and is represented as E_(nx,ny,nz) = (n_x+n_y+n_z+1.5)*[h-]*ω or Energy Eigen Values of 3D SHO = (Energy Levels of 3D Oscillator along X axis+Energy Levels of 3D Oscillator along Y axis+Energy Levels of 3D Oscillator along Z axis+1.5)*[h-]*Angular Frequency of Oscillator. Energy Levels of 3D Oscillator along X axis are the quantised energy levels in which a particle may be present, Energy Levels of 3D Oscillator along Y axis are the quantised energy levels in which a particle may be present, Energy Levels of 3D Oscillator along Z axis are the quantised energy levels in which a particle may be present & Angular Frequency of Oscillator is the angular displacement of any element of the wave per unit of time or the rate of change of the phase of the waveform.

How to calculate Energy Eigen Values for 3D SHO?

The Energy Eigen Values for 3D SHO formula is defined as the energy that a particle possess residing in that quantised energy level is calculated using Energy Eigen Values of 3D SHO = (Energy Levels of 3D Oscillator along X axis+Energy Levels of 3D Oscillator along Y axis+Energy Levels of 3D Oscillator along Z axis+1.5)*[h-]*Angular Frequency of Oscillator. To calculate Energy Eigen Values for 3D SHO, you need Energy Levels of 3D Oscillator along X axis (n_x), Energy Levels of 3D Oscillator along Y axis (n_y), Energy Levels of 3D Oscillator along Z axis (n_z) & Angular Frequency of Oscillator (ω). With our tool, you need to enter the respective value for Energy Levels of 3D Oscillator along X axis, Energy Levels of 3D Oscillator along Y axis, Energy Levels of 3D Oscillator along Z axis & Angular Frequency of Oscillator and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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