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Energy Eigen Values for 3D SHO Formula

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Energy Eigen Values of 3D SHO is the energy possessed by a particle residing in the nx, ny and nz energy levels. Check FAQs

E (nx,ny,nz) = (n x + n y + n z + 1.5) \cdot [h-] \cdot ω

E_(nx,ny,nz) - Energy Eigen Values of 3D SHO?n_x - Energy Levels of 3D Oscillator along X axis?n_y - Energy Levels of 3D Oscillator along Y axis?n_z - Energy Levels of 3D Oscillator along Z axis?ω - Angular Frequency of Oscillator?[h-] - Reduced Planck constant?

Energy Eigen Values for 3D SHO Example

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Here is how the Energy Eigen Values for 3D SHO equation looks like with Values.

Here is how the Energy Eigen Values for 3D SHO equation looks like with Units.

Here is how the Energy Eigen Values for 3D SHO equation looks like.

1.3E-33 = (2 + 2 + 2 + 1.5) \cdot 1.1E-34 \cdot 1.666

1.3E-33J = (2 + 2 + 2 + 1.5) \cdot 1.1E-34 \cdot 1.666rad/s

1.3E-33 = (2 + 2 + 2 + 1.5) \cdot 1.1E-34 \cdot 1.666

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Energy Eigen Values for 3D SHO Solution

Follow our step by step solution on how to calculate Energy Eigen Values for 3D SHO?

FIRST Step Consider the formula

E (nx,ny,nz) = (n x + n y + n z + 1.5) \cdot [h-] \cdot ω

Next Step Substitute values of Variables

∴

E (nx,ny,nz) = (2 + 2 + 2 + 1.5) \cdot [h-] \cdot 1.666rad/s

Next Step Substitute values of Constants

∴

E (nx,ny,nz) = (2 + 2 + 2 + 1.5) \cdot 1.1E-34 \cdot 1.666rad/s

Next Step Prepare to Evaluate

∴

E (nx,ny,nz) = (2 + 2 + 2 + 1.5) \cdot 1.1E-34 \cdot 1.666

Next Step Evaluate

∴

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

LAST Step Rounding Answer

∴

E (nx,ny,nz) = 1.3E-33J

Energy Eigen Values for 3D SHO Formula Elements

Variables

Constants

Energy Eigen Values of 3D SHO

Energy Eigen Values of 3D SHO is the energy possessed by a particle residing in the nx, ny and nz energy levels.

Symbol: E_(nx,ny,nz)

Measurement: EnergyUnit: J

Note: Value can be positive or negative.

Formulas to find Energy Eigen Values of 3D SHO

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.

Symbol: n_x

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Energy Levels of 3D Oscillator along X axis

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.

Symbol: n_y

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Energy Levels of 3D Oscillator along Y axis

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.

Symbol: n_z

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Energy Levels of 3D Oscillator along Z axis

Angular Frequency of Oscillator

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.

Symbol: ω

Measurement: Angular FrequencyUnit: rad/s

Note: Value can be positive or negative.

Formulas to find Angular Frequency of Oscillator

Reduced Planck constant

Reduced Planck constant is a fundamental physical constant that relates the energy of a quantum system to the frequency of its associated wave function.

Symbol: [h-]

Value: 1.054571817E-34

Other formulas in Simple Harmonic Oscillator category

Go Restoring Force of Diatomic Vibrating Molecule

F = - (k \cdot x)

Go Potential Energy of Vibrating Atom

V = 0.5 \cdot (k \cdot {(x)}^{2})

Go Energy Eigen Values for 1D SHO

E n = (n + 0.5) \cdot ([h-]) \cdot (ω)

Go Zero Point Energy of Particle in 1D SHO

Z.P.E = 0.5 \cdot [h-] \cdot ω

How to Evaluate Energy Eigen Values for 3D SHO?

Energy Eigen Values for 3D SHO evaluator 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 evaluate 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 evaluate Energy Eigen Values for 3D SHO using this online evaluator? To use this online evaluator 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.

FAQs on Energy Eigen Values for 3D SHO

What is the formula to find Energy Eigen Values for 3D SHO?

The formula of Energy Eigen Values for 3D SHO is expressed as 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. Here is an example- 1.3E-33 = (2+2+2+1.5)*[h-]*1.666.

How to calculate Energy Eigen Values for 3D SHO?

With 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) we can find Energy Eigen Values for 3D SHO using the formula - 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. This formula also uses Reduced Planck constant .

Can the Energy Eigen Values for 3D SHO be negative?

Yes, the Energy Eigen Values for 3D SHO, measured in Energy can be negative.

Which unit is used to measure Energy Eigen Values for 3D SHO?

Energy Eigen Values for 3D SHO is usually measured using the Joule[J] for Energy. Kilojoule[J], Gigajoule[J], Megajoule[J] are the few other units in which Energy Eigen Values for 3D SHO can be measured.

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Energy Eigen Values for 3D SHO Formula

Energy Eigen Values for 3D SHO Example

Energy Eigen Values for 3D SHO Solution

Energy Eigen Values for 3D SHO Formula Elements

Other formulas in Simple Harmonic Oscillator category

How to Evaluate Energy Eigen Values for 3D SHO?

FAQs on Energy Eigen Values for 3D SHO

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