Creating Non-Clustered Index on Non-Persisted Computed Column SQL Server

I am struggling to find any documentation on how SQL Server actually stores a non-persisted computed column.

Take the following example:

--SCHEMA
CREATE TABLE dbo.Invoice
(
    InvoiceID INT IDENTITY(1, 1) PRIMARY KEY,
    CustomerID INT FOREIGN KEY REFERENCES dbo.Customer(CustomerID),
    InvoiceStatus NVARCHAR(50) NOT NULL,
    InvoiceStatusID AS CASE InvoiceStatus 
                         WHEN 'Sent' THEN 1 
                         WHEN 'Complete' THEN 2
                         WHEN 'Received' THEN 3
                       END
)
GO

--INDEX
CREATE NONCLUSTERED INDEX IX_Invoice ON Invoice
(
    CustomerID ASC
)
INCLUDE
(
    InvoiceStatusID
)
GO

I get that it is stored at the leaf level, but if the value is not persisted how is anything stored at all? How does the index help SQL Server find these rows in this situation?

Any help greatly appreciated,

Many Thanks,

EDIT:

Thanks to Brent & Aaron for answering this, here's the PasteThePlan clearly showing what they explained.

When SQL Server creates the index on the computed field, the computed field is written to disk at that time - but only on the 8K pages of that index. SQL Server can compute the InvoiceStatusID as it reads through the clustered index - there's no need to write that data to the clustered index.

As you delete/update/insert rows in dbo.Invoice, the data in the indexes is kept up to date. (When InvoiceStatus changes, SQL Server knows to also update IX_Invoice.)

The best way you can see this for yourself is to actually do it: create these objects, and execute updates that touch the InvoiceStatusID field. Post the execution plan (PasteThePlan.com is helpful for this) if you want help seeing where the index updates are happening.

StackExchange Database Administrators Q#163528, answer score: 11